# Talk:Fermat's Last Theorem

## Guinness book of world records comment

What relevance is it that the GB of WR thought it was a difficult problem? I certainly don't feel it is noteworthy enough to be the closing remark of the opening paragraph 81.155.163.64 (talk) 16:44, 16 May 2014 (UTC)

## This problem has been solved

I feel like I should bring up that 3,987^12 + 4,365^12 = 4,472^12 — Preceding unsigned comment added by 70.176.190.25 (talk) 06:56, 7 November 2013 (UTC)

Close, but no. The left and right sides differ by 1211886809373872630985912112862690. Try it in Python or some other system like it that supports unlimited precision integers automatically. —David Eppstein (talk) 07:18, 7 November 2013 (UTC)
Or just notice that 3987 and 4365 are both multiples of 3, but 4472 is not.—GraemeMcRaetalk 00:03, 10 November 2013 (UTC)
The American might be trying to waste our time, as an alleged joke. — Preceding unsigned comment added by 46.64.108.104 (talk) 13:33, 21 September 2014 (UTC)
I think it is a reference to a popular cartoon series: it is also referred to in this Zbl 0991.11072. Deltahedron (talk) 16:06, 21 September 2014 (UTC)

## Wiles's Proof of FLT?

Ribet proves that Frey's elliptic equation is non modular (and it and Fermat's equality do not exist). Wiles proves that all elliptic equations are modular (and since Frey's elliptic equation is non modular Fermat's equality does not exist). Looks like Wiles has proved what Ribet proved does not exist, namely, Fermat's equality. Moreover, why is Wiles's proof of modularity superior to Ribet's counter example? And, why does modularity rather than existence determine Wiles's proof? Jamestmsn (talk) 23:44, 29 February 2012 (UTC)

Ribet proved that if a (nontrivial) solution to Fermat's equation exists, then the Frey curve that can be defined from it would semistable and not be modular; it is a conditional statement. Wiles proved that all semi-stable elliptic curves are modular; this is enough to establish Fermat's Last Theorem, but only thanks to Ribet's Theorem. Ribet did not show that there are no solutions to Fermat's equation. Wiles's Theorem is not directly about Fermat's Last Theorem, but rather about elliptic curves. Magidin (talk) 03:21, 1 March 2012 (UTC)

How does Ribet's theorem become "enough to establish Fermat's Last Theorem? The Wiles modularity – Ribet non modularity contradiction is not relevant to the issue whether Frey's elliptical curve, and its source Fermat's equality, exist as solutions. To prove FLT, Wiles assumes Frey's curve does not exist thanks to Ribet's theorem. However, the fact that Frey's curve is non modular does not change the fact that it is elliptical. Elliptical curves are defined by their forms and coefficients not by their modularity. Frey's elliptical curve does not disappear by the fact it is non modular. Its form and coefficients depend from Fermat's equality thanks to Frey's work not to non modularity thanks to Ribet's theorem. Simply put, to prove FLT, Wiles uses the irrelevant contradiction between his work and Ribet's work to conclude, without proof, that Frey's curve and Fermat's equality are forbidden to exist. 72.87.171.201 (talk) 18:26, 2 March 2012 (UTC)

Sigh... This is not the proper place for this discussion; Talk pages are not a forum. I will simply note that you are completely misunderstanding what "Frey's curve" is (in fact, it does not exist; it can only be defined if there is a nontrivial solution to the Fermat equation). Because the definition assumes that you have ${\displaystyle y^{2}=x(x-a^{p})(x-b^{p})}$ and that ${\displaystyle a^{p}+b^{p}}$ is a pth power of an integer. That is, that there is a c such that ${\displaystyle a^{p}+b^{p}=c^{p}}$. Without those properties, you are not looking at "the" Frey curve, you are looking at some elliptic curve.
The chain of argument is: If there is a nontrivial solution to Fermat's equation, then C exists (Frey); if C exists, then C is semistable and not modular (Ribet). All semi-stable elliptic curves are modular. (Wiles). Using contrapositives and modus ponens, the conclusion is "There is no nontrivial solution to Fermat's equation." If you wish to learn about this, then go to an appropriate place and stop using the talk page for it. Meanwhile, I'll simply note that you don't know what you are talking about. Magidin (talk) 19:24, 2 March 2012 (UTC)

Stick to the point and answer the question. How does Ribet's theorem become "enough to establish Fermat's Last Theorem"? Ribet's theorem proves (1) Frey's elliptical equation (FEE) is an exception to Wile's modularity theorem and (2) FEE is not connected to a modular form. (1) disproves Wile's modularity theorem and (2) is not relevant to establishing Fermat's Last Theorem. Note that FEE is based on an existence proof which assumes if Fermat's equality (FE) exists then FEE exists. However, how do we know that FEE is dependent solely on FE? For example, one does not need FE to study FEE in the abstract. Conditional FE, therefore, is not relevant to and does not make FEE conditional for any purpose. 72.87.171.215 (talk) 19:25, 4 March 2012 (UTC)

I answered the question; you just didn't understand it. And talk pages are not a forum for discussion of the subject matter of the article. Take it somewhere else. This is not the appropriate place for you to discuss this. Magidin (talk) 20:59, 4 March 2012 (UTC)

Actually I think Jamestmsn is asking reasonable questions here, and pointing out that the article is a little unclear. I've just made an edit that I hope resolves the issue. The phrase "the above elliptic curve is always non-modular" certainly gives the impression that the elliptic curve in question exists. What Ribet proved (if I understand correctly) is that if such an elliptic curve existed, then it wouldn't be modular. Wiles proved that if such an elliptic curve existed then it would be modular (because all semistable elliptic curves are modular). Because of the contradiction, we have to assume that Frey's elliptic curve can't exist (or that Ribet or Wiles or someone made a mistake). In other words, Wiles didn't assume the non-existence of Frey's curve, he proved that it can't exist. Jowa fan (talk) 06:01, 5 March 2012 (UTC)

It is really quite straightforward:
1. If Fermat's Last Theorem is false then a counterexample exists.
2. If a counterexample to FLT exists then an associated elliptic curve (the "Frey curve") is rational, semistable and non-modular.
But Wiles proved that all rational, semistable elliptic curves are modular. Therefore there is no Frey curve that is rational, semistable and non-modular. Therefore a counterexample to FLT does not exist. Therefore FLT is true. Gandalf61 (talk) 09:00, 5 March 2012 (UTC)

Ribet's theorem disproves Pythagoras theorem. Simply write Fermat's equality in Pythagorean form (c^p/2)2=(a^p/2)2+(b^p/2)2 and assume p is an even number. 72.87.171.165 (talk) 17:08, 6 March 2012 (UTC)

For the third time: your edits in this page are disruptive and violate Wikipedia policy. Talk pages are not a forum. There are plenty of websites and discussion boards where you can be enlightened about these issues if you really want to learn something. This is not one of them. Magidin (talk) 18:11, 6 March 2012 (UTC)

Where can I find a website "where you can be enlightened about these issues if you really want to learn something" about Pythagoras theorem? 72.87.171.186 (talk) —Preceding undated comment added 23:27, 26 March 2012 (UTC).

Probably 6½ years too late now, but an answer for anyone else: https://math.stackexchange.com/ PJTraill (talk) 12:29, 8 October 2018 (UTC)

## Single Page Proof of FLT?

See at http://www.coolissues.com/mathematics/BealFermatPythagorasTriplets.htm Jamestmsn (talk) 04:44, 5 March 2012 (UTC)

Regardless of the (lack of) correctness of the content of that page: (i) The talk page is not a forum for general discussion. (ii) The material there does not abide by the Wikipedia policies for inclusion: it is not a reliable source. (iii) If the page is yours, then you are talking about original research, also against Wikipedia policy, and self-promotion. (iv) You are engaging in link spam. Magidin (talk) 20:05, 5 March 2012 (UTC)

## This talk page needs any special message??

People keep coming here showing their proof of FLT, but they always get reverted saying "This talk page is for article improvements ONLY." Does this talk page need a special banner?? Georgia guy (talk) 19:29, 22 July 2012 (UTC)

That's part of the basic Wikipedia policy on talk pages. I doubt that people who post from IP addresses, and often repeatedly re-post the same stuff here after it's been deleted and the issue been explained to them, will be detered by a banner telling them not to. I have yet to see someone who posts such stuff even apologize after it's been pointed out to them that's not what the talk page is for... But if you have such a banner, I guess it can't hurt to add it. Magidin (talk) 20:11, 22 July 2012 (UTC)

## Fermat's theorem for even exponents

This article mentions an elementary proof by Guy Tarjanian for even exponents. In the reference we are said to find it in the "Comptes rendus hebdomadaires des séances de l'Académie des sciences" 1977-series. It just so happens that this series seems to be digitalised on a french website http://gallica.bnf.fr/?lang=EN. Yet, I can not find Tarjanian's result itself. Can anyone help? — Preceding unsigned comment added by 193.190.253.144 (talk) 11:37, 4 September 2012 (UTC)

It is listed out of order in the corresponding page; look at the volume that says 1977/07 (T285, N16)-1977/12, which is the first one listed in volume 285 (rather than the last, where you might expect it). It is probably listed first because this issue contains the table of contents and author list for the whole volume. Magidin (talk) 15:25, 4 September 2012 (UTC)

Thanks for helping. — Preceding unsigned comment added by 62.235.150.40 (talk) 17:48, 4 September 2012 (UTC) I've found it by now. I've not yet read the content, but I'm wondering what this theorem has to do with Fermat's. It says: if for some integers x,y,z and an odd prime p x^(2p)+y^(2p) = z^(2p) then 2p must divide x or y. That doesn't rule out the possibility that there exist coprime x,y,z with 2p dividing x (so 2 nor p divides y or z) and such that x^(2p) + y^(2p) = z^(2p). — Preceding unsigned comment added by 62.235.150.40 (talk) 17:43, 4 September 2012 (UTC)

Fermat's Last Theorem was traditionally divided into two cases, Case I (in which odd prime factors of ${\displaystyle n}$ do not divide ${\displaystyle xyz}$), and Case II (in which there is an odd prime factor of ${\displaystyle n}$ that does divide ${\displaystyle xyz}$). The result thus establishes Case I for exponent p (if you had that p divides z, then by rewriting the equation as ${\displaystyle y^{2p}+(-z)^{2p}=(-x)^{2p}}$ you would get a contradiction, so the result actually shows that Case I cannot occur). That is, it is related to Fermat's Last Theorem (along classical lines). That said, Case I was generally easier than Case II. Magidin (talk) 20:46, 4 September 2012 (UTC)

Ok, I understand. But these two cases aren't explained in the article as far as I see, so I think you should either write a section about them or (if you judge this too specialised for wikipedia) remove the reference to Tarjanian's result alltogether as it will surely confuse other readers too. — Preceding unsigned comment added by 62.235.150.40 (talk) 10:24, 5 September 2012 (UTC)

Ok, I see what you mean. But still: In the sentence "As a byproduct of this latter work, she [Germain] proved Sophie Germain's theorem, which verified the first case of Fermat's Last Theorem (the case in which p does not divide xyz)" might mean that the case described between brackets is a subcase of a particular (undescribed) case 1. Besides, I appreciate the work you're doing and it is not my intention to randomly criticise your work. I do not know how to produce signed comments, but I'll try to figure it out myself. — Preceding unsigned comment added by 62.235.150.40 (talk) 21:20, 5 September 2012 (UTC)

I explained how to sign your comments: write four tildes at the end, like so: ~~~~. This will automatically produce the signature, just like I explained. I honestly do not see how that reading is even feasible; the sentence says "first case", and then immediately describes a condition. How could it possibly be understood to mean "a subcase of the first case"? Of course, if one really wants to misunderstand, I'm sure one will find a way of doing so, even after I add a "namely" to the parenthetical remark. Magidin (talk) 05:26, 6 September 2012 (UTC)
Is there another integer triplet than (1,2,3) for x^3+y^3=z^2? Thanks for an answer. 174.95.63.159 (talk) 01:22, 22 April 2013 (UTC)
This is not the place to ask such a question; the talk page is exclusively to discuss improvements to the article in Wikipedia. If you wish to ask a mathematics question, or have a discussion, then there are other places where it can be done, such as math.stackexchange.com. Magidin (talk) 02:20, 22 April 2013 (UTC)
Can you make an exception? Please direct me to wherever or whomever, and then delete my posts as well as yours as if nothing had happened. I got nowhere so I end up here. 174.95.63.159 (talk) 12:19, 22 April 2013 (UTC)
No, I can't make an exception. I already directed you to an appropriate site in which you can post your question: math.stackexchange.com. Magidin (talk) 14:54, 22 April 2013 (UTC)
Thank you. I will go there. Please delete all the exchanges between you and me.174.95.63.159 (talk) 21:27, 22 April 2013 (UTC)
I am surprised that you have not deleted my posts. Anyway, I went there. Several friendly people offered their results. They inspired me, and I have found an algorithm myself. I will try positive integers f and g until f^3+g^3= k×h^2. Then a triplet is (kf)^3+(kg)^3=(hk^2)^2. For example, 3^3+5^3=4×38. A triplet emerges as 114^3+190^3=2888^2. If my post has violated the rule, please delete it. 174.95.63.159 (talk) 04:53, 24 April 2013 (UTC)
Large scale removal of content from talk pages is discouraged. I am not inclined to do so. At the very least, it will stand here for a while (until automatically archived for lack of activity, hint, hint) as a possible deterrent for others who would post here without bothering to read the explanations of what Wikipedia is and what it is not, and what talk pages are for. Magidin (talk) 15:29, 24 April 2013 (UTC)
If I did not stumble upon you, who would have directed me to that web site? In this case, everyone is in a win-win situation. :-) 174.95.63.159 (talk) 19:59, 24 April 2013 (UTC)
Are you kidding me? Doesn't take too much ingenuity to find appropriate websites to ask questions, nor does it take too much of your time to bother reading the policy materials for Wikipedia before stomping around. So thank you for doing so. And for reading the reply you first got so carefully that I was forced to repeat the information twice before you noticed it. It's a win for you because you got what you wanted; it's a lose for me, because not only did I need to spend time educating you as to the nature of Wikipedia, in addition it is clear that you did not learn anything other than that you can do as you please and get what you want anyway. Magidin (talk) 20:38, 24 April 2013 (UTC)
What's the matter with you, to reply to me like that? 23:16, 25 April 2013 (UTC) — Preceding unsigned comment added by 174.95.67.39 (talk)

## New comment

You seem to be under the impression that it is possible for an integer to simultaneously be an odd prime and contain a factor of 4, which confuses me to some extent, though i admit i do not have the background in mathematics most of you probably do.201.196.189.134 (talk) 07:13, 6 April 2013 (UTC)

Who are you talking to? What are you refering to? Magidin (talk) 20:18, 6 April 2013 (UTC)

## Deleted reference

A few days ago I removed the following reference that had been added to the Further Reading section:

Sinyor, Joseph with Ted Speevak and Akalu Tefera (received June 2000). "A New Combinatorial Identity". International Journal of Mathematics and Mathematical Sciences. ISBN 25:6 (2001) 361–363 S0161171201005361 Check `|isbn=` value: invalid character (help). Check date values in: `|date=` (help)

The reference was added by the first author. I removed it for several reasons:

• Conflict of interest: The author of the paper adding a reference to his own paper as a "further reading".
• Undue weight: The Further Reading section currently contains references to major works (books by Edwards, Aczel, Dickson, Mordell, Ribenboim) and important surveys (Faltings, Saikia). This paper seems out of place there, dealing as it does with some partial results that are "related to" Fermat's equation.
• Lack of notability: I also note that although the paper is indexed by MathSciNet, it did not merit a full review (the MathReview quotes the abstract only), and MathSciNet does not record any references to the paper; Zentralblatt likewise only quoted the abstract. While these may not be fully dispositive of whether this paper is notable or not, I believe they are indicative and place the burden of proof on someone who wishes to add the paper to the list of "Further Reading" to establish its notoriety.

The editor who added the paper (who is also one of the authors) then proceeded to track down my e-mail address and e-mail me directly asking me to "reconsider" the addition; I advised him to make his case here in the talk page rather than personally to me. As he has not done so, I'm adding my justification for the deletion for the record. Magidin (talk) 16:42, 19 October 2012 (UTC)

My name is Joseph Sinyor and I made the edit mentioned. In 2001 I published a paper in the IJMMS on a new combinatorial identity (along with two co-authors - one of whom is a professional mathematician) which is indeed "related" to FLT. In the 1820's it was noted that (xn + yn - zn) would produce 3 equations which would have to be satisfied for a counter-example to exist to FLT. Using our new identity one can now add a fourth equation to this list. I have no idea if this could lead to any insight into a possible elementary proof or Fermat's thinking, but feel it is worth at least bringing it to the attention of lovers of number theory, amateur or professional. This paper is therefore not about just another of "thousands" of identities. I made the edit myself in an effort at transparency and put it in "further reading" - I did not create the categories and the reviewer could have been charitable & placed the reference elsewhere. When I contacted him privately (precisely because I wished to avoid acrimonious communications) I was told I would have to "prove" the identity was worth listing among the otherwise august list of other works. Obviously there is nothing I can add to my paper that will convince him (MathSciNet probably did not review it because they also saw it as just another identity).
I feel I am now entitled to some self-promotion here: if you liked this paper, read my paper on the 3x+1 problem by googling me.Jojosinyor (talk) 02:08, 22 October 2012 (UTC)
Regarding your final paragraph (I will not further opine on the rest and let other editors comment): it is out of place in the talk page. Please read the Wikipedia Talk Page guidelines, specifically the point that talk pages are not a forum. Self-promotion is simply out of place. Talk pages exist for the purpose of discussing improvements to the article, not for you to publicize your work. If you want to use the internet to publicize your work, please set up a personal blog. Magidin (talk) 02:41, 22 October 2012 (UTC)

## Down Goes Brown reference

I'm not sure exactly what the criteria for a blog post are, but the entries (including this one) also appear in the National Post, one of Canada's two main national daily newspapers. Does that get you to notability? Silverpie (talk) 20:13, 11 January 2013 (UTC)

## Simplification

Forgive the lack of good editing policy, as I am a very infrequent editor of Wikipedia. It's just that I had been watching some Numberphile videos about Fermats last theoreom which sparked me to find this article again: http://www.sciencedaily.com/releases/2013/03/130304105652.htm

I think it warrants inclusion into the article (and possibly some others in regards to maths proofs). It discusses drastic changes to structure of the proof, and provides a new way of proving it that is notable and more likely to be accessible--In other words, it might also be worthy of its own page. Gödel's Prodigal Apprentice (talk) 06:08, 2 October 2013 (UTC)

First, I don't think you understand what is being claimed in the article; I do not see how what is being proposed is "a new way of proving [FLT]" or that it is "more likely to be accessible". The issue is actually a rather technical one of exactly which axioms of set theory are needed to support the proof. As I understand the article, he does not propose any changes to the general structure of the proof, nor any new way of proving it; he is just saying that one can justify the set-theoretic arguments used using a relatively small fraction of Axiomatic Set Theory, as opposed to an enriched theory (which underlies some of Grothendieck's work). This is a very technical issue, of interest to some model theorists and people in mathematical logic, but unlikely to be of general interest even within mathematics (very few people within mathematics care right now about exactly how much Set Theory Wiles needs to get his proof through!) Second, a news report is not a reliable source for the purpose of mathematical claims. If and when the work gets peer reviewed and suitably sourced, it might be relevant. Magidin (talk) 15:52, 2 October 2013 (UTC)
By the way, I think this talk section's title is seriously misleading. Reworking the proof to use fewer set-theoretic assumptions is very unlikely to be a simplification. —David Eppstein (talk) 17:45, 2 October 2013 (UTC)
PS the comments about one-handed pottery in this interview may be relevant. —David Eppstein (talk) 03:57, 4 October 2013 (UTC)

## Capital T

On the naming conventions for theorems (which is no longer relevant) it does point out the the L in last is a possible grey area for the normal capitalization rules. Fine, but why is the T in theorem capitalized? As far as I can tell (looking at the list of theorems) there is no other example of a theorem on wikipedia with that characteristic and is in clear violation of WP:NCCAPS (as is the capital L really, imo). Opinions? Wgunther (talk) 21:29, 20 October 2013 (UTC)

## Page move

moved the page from Fermat's Last Theorem to Wiles-Fermat Theorem [1]. I've never heard the theorem referred to under this name so I think it should be moved back, but I think it would be better to gain some consensus before starting a move-war.--User:Salix alba (talk): 11:53, 30 October 2013 (UTC)

I've never head it called that either. Google returns 1870 hits. Even "Wiles Theorem"[sic] gets more hits (2460), and would be far more accurate than "Wiles-Fermat". "Fermat's Last Theorem" gets over 381000 hits. I oppose the move; things are called what they are called, not what they ought to be called. I don't see the Pell's equation page being moved around to account for Euler's mis-attribution. Magidin (talk) 15:33, 30 October 2013 (UTC)
I also oppose the move. This is not the place to advocate for replacement of standard terminology by neologisms, even when those neologisms would be more accurate; see WP:SOAPBOX. This should be reverted. —David Eppstein (talk) 16:23, 30 October 2013 (UTC)

A second a third opinion is good enough for me. Move reverted.--User:Salix alba (talk): 17:32, 30 October 2013 (UTC)

Of course. Paul August 10:47, 6 November 2013 (UTC)

## Why Fermat did not have a proof

I have seen the suggestion (hinted at in the section Fermat's Last Theorem#Fermat's conjecture) that a reason to feel confident that Fermat did not have a proof is that he did not challenge other people to prove it, as appears to have been his wont. I thought it might have been in Alf van der Poorten’s book, but a skim has just failed to throw it up; perhaps it is in Singh’s. If anyone has a good source for it, I think it would be worth mentioning in the section Fermat's Last Theorem#Did Fermat possess a general proof?, as I have observed that that question is often raised, along with the suggestion “People ought to be trying find his proof”. It would also enable us to remove the “{{citation-needed}}” (if we reworded the formulation). I have in any case moved the the latter section to be a sub-section of the former, and removed some of the redundancy this made evident. PJTraill (talk) 23:58, 4 March 2014 (UTC)

Dealt with: Casually glancing at van der Poorten again, I saw the very place, and have included references to that and to Weil in Fermat's Last Theorem#Did Fermat possess a general proof? and removed the “most mathematicians and historians” remark, with its {{citation-needed}}. I have instead asserted that it “appears unlikely” that he had a general proof; I hope it is sufficiently evident that that bald statement is justified by the rest of the section without encumbering it with “for the following reasons”. PJTraill (talk) 11:10, 6 March 2014 (UTC)
This discussion has been closed. Please do not modify it.
The following discussion has been closed. Please do not modify it.

Fermat did have a solution to his conjecture. The hint is in A^2 + B^2 = C^2, which has only one solution set: A = 2 * X + 1, B = 2 * X * (X + 1), C = B + 1. The proof is in the general form of the natural exponential function: x^y = f(x,y,y) f(1,y,p) = 1 f(x,y,p) = f(x-1,y,p) + 1 + g(x,y-1,p) g(1,y,p) = 0 g(x,1,p) = g(x-1,1,p) + d(x,p) g(x,y,p) = g(x-1,y,p) + g(x,y-1,p) d(x,p) = p ! - [decay function of p!]. The primary component of this function requires the addition of 1 to the secondary result, which makes generating a valid result above power 2 impossible. (As shown above, squares have their limitations, too.) Note: This only works in the Natural domain. James Harris Mowbray, USA. — Preceding unsigned comment added by 71.163.125.101 (talk) 15:57, 13 September 2018 (UTC)

This is at best original research, and unsuitable for inclusion. Magidin (talk) 16:08, 13 September 2018 (UTC)

Other than the fact that it is a valid solution? Reduced forms:

``` f(x,2,2) = f(x-1,2,2) + 1 + 2 * (x - 1)
f(x,3,3) = f(x-1,3,3) + 1 + 3 * x * (x - 1)
```

Just an idea. And a solution Fermat could have come up with. — Preceding unsigned comment added by 71.163.125.101 (talk) 03:48, 14 September 2018 (UTC)

Talk pages are not a forum for general discussion. Wikipedia is not an outlet for original research. The threshold for inclusion in Wikipedia is verfiability (through appropriate verifiable sources), not truth. I have not checked your work nor do I intend to. It is inappropriate for inclusion, and your entire contribution to this talk page so far is inappropriate. Magidin (talk) 06:18, 14 September 2018 (UTC)

## Does Fermat's copy of Arithmetica, writing in the margin and all, still exist?

This should probably be mentioned somewhere. I couldn't find a reference to it in the article Shiggity (talk) 19:47, 12 May 2014 (UTC)

## The least number of n-power numbers (A new conjecture)

${\displaystyle a_{1}^{n}+a_{2}^{n}+a_{3}^{n}+...+a_{m}^{n}=b^{n}}$

n=2, m>=2

n=3~4, m>=3

n=5~8, m>=4

n=9~16, m>=5

n=17~32, m>=6

......

m>=${\displaystyle |[-log_{2}(n)]|+1}$

Is it true??? — Preceding unsigned comment added by 140.113.136.220 (talk) 02:10, 19 May 2014 (UTC)

This forum is for discussing improvements to the encyclopedia article on Fermat's Last Theorem, not on discussing potential improvements to the theorem itself. —David Eppstein (talk) 03:13, 19 May 2014 (UTC)

## Possible incorrect statement or wording

The section on proofs for specific exponents states "[Fermat] uses the technique of infinite descent to show that the area of a right triangle with integer sides can never equal the square of an integer." A right triangle with sides 10 and 20 has an area of 100, which is the square of the integer 10, contradicting what this claims Fermat had shown. Perhaps there were more conditions to what he demonstrated (the sides of the triangle must be primes?) or the wording here is prone to serious misinterpretation.209.197.173.154 (talk) 00:52, 15 June 2014 (UTC)

All three sides need to be integer length, not just the legs. In your example the hypotenuse has length 10√5, which is not an integer. Lagrange613 05:03, 15 June 2014 (UTC)

I have changed the video link to the documentary on You Tube (which had gone dead because of BBC copyright) to a link to vimeo.com, but am not sure if that is in breach of copyright. The BBC itself offers the documentary at http://www.bbc.co.uk/programmes/b0074rxx, but that apparently only works in the UK. Should we actually use that? PJTraill (talk) 22:18, 19 December 2014 (UTC)

## Reverted pending discussion

User 173.174.176.65 deleted the entire section on Subsequent developments and solution, claiming it was done "to simplify". Then added claims, such as that the full proof of the Taniyama-Shimura modularity conjecture is "impossible to check even with computers", without any citation (I have not heard that claim made anywhere, has anyone?); and alleged connections between the Last Theorem and the "polygonal number conjecture", again with no references or citation. I've reverted; while some of the minor changes might be reasonable, I don't think such large deletions should be done without a discussion and consensus, and certainly the kind of assertions I cited above would need some good reliable sources before being added on the say so of an anonymous editor. Magidin (talk) 23:56, 30 December 2014 (UTC)

## A special case of this theorem

If 2n+1 is prime (n>1), than ${\displaystyle x^{n}+y^{n}=z^{n}}$ has no solutions which none of x, y, and z are divisible by 2n+1, because if x is not divisible by 2n+1, than xn must congruent to +1 or -1 to mod 2n+1, so do y and z, and x^n + y^n ≠ z^n (mod 2n+1), since (+1) + (+1), (+1) + (-1), (-1) + (+1), and (-1) + (-1), are not congruent to +1 or -1 (mod 2n+1), because of 2n+1 > 3.

This can prove this theorem for n = 3, 5, 6, 8, 9, 11, 14, 15, 18, 20, 21, 23, 26, 29, 30, 33, 35, 36, 39, 41, 44, 48, 50, 51, 53, 54, 56, 63, 65, 68, 69, 74, 75, 78, 81, 83, 86, 89, 90, 95, 96, 98, 99, 105, 111, 113, 114, 116, 119, 120, 125, 128, 131, 134, 135, 138, 140, 141, 146, 153, 155, 156, 158, 165, 168, 173, 174, 176, 179, ... and their multiples. — Preceding unsigned comment added by 49.215.193.189 (talk) 03:14 January 31 2015 (UTC)

The primes n for which 2n+1 is also prime are called Sophie Germain primes, and Sophie Germain proved back in the early 19th century that there is no solution to the Fermat equation when n is such a prime and in which n does not divide xyz. In other words, she proved exactly what you write above. :In any case, the talk page is for discussing improvements to the article, which must be appropriately sourced and verifiable. This comment is neither. Magidin (talk) 01:11, 1 February 2015 (UTC)

## Could Fermat Have Had the Proof?

The article leaves the question open as to whether he actually had the proof or not. As a reader, I would like to know if, in retrospect "experts" agree that he either could or could not have had the proof found in 1994. I wonder if the proof required advances in mathematics that Fermat may not have been aware of, or if he actually did have the "tools" needed for the proof and it took 300+ years to put them to use. Hope this makes sense. What I'm looking for is consensus either way, or a direct statement that there is no consensus on whether or not Fermat could (or could not) have had the proof prior to it's 1994 discovery.Jonny Quick (talk) 09:05, 11 June 2015 (UTC)

In the section Fermat's Conjecture, it states:
"It is not known whether Fermat had actually found a valid proof for all exponents n, but it appears unlikely. Only one related proof by him has survived, namely for the case n = 4, as described in the section Proofs for specific exponents. While Fermat posed the cases of n = 4 and of n = 3 as challenges to his mathematical correspondents, such as Marin Mersenne, Blaise Pascal, and John Wallis,[19] he never posed the general case.[20] Moreover, in the last thirty years of his life, Fermat never again wrote of his "truly marvellous proof" of the general case, and never published it. Van der Poorten[21] suggests that while the absence of a proof is insignificant, the lack of challenges means Fermat realised he did not have a proof; he quotes Weil[22] as saying Fermat must have briefly deluded himself with an irretrievable idea. The techniques Fermat might have used in such a "marvellous proof" are unknown. Taylor and Wiles’s proof relies on 20th century techniques.[23] Fermat’s proof would have had to have been elementary by comparison, given the mathematical knowledge of his time."
Why is this not a direct answer to your questions? Yes: the proof as is known today requires advances in mathematics that were well beyond Fermat's knowledge and he lacked the tools that were actually used (he lacked the tools needed to produce the tools needed to produce... to produce the tools that were used in the proof). And it is generally thought that he probably did not have one, as indicated by the paragraph above. Magidin (talk) 17:02, 11 June 2015 (UTC)
The compelling reason is that Fermat's claim to have solved it is a big part of the fame of this problem. —David Eppstein (talk) 07:44, 13 June 2015 (UTC)
One would have to explain why it is called "Fermat's last theorem"; that's important, and should be in the lead. The fact is that it is called that because of Fermat's margin note in the book which is Fermat's claim to have a "truly marvelous proof". Magidin (talk) 21:30, 13 June 2015 (UTC)

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## Statement

The article had the following two formal statements of the problem:
xn + yn = zn, where n ≥ 3, has no non-trivial solutions x, y, zN, and
xn + yn = zn, where n ≥ 3, has no non-trivial solutions x, y, zZ.
I have seen these before, and again here, but I do not understand how these are correct formal statements of the theorem. Shouldn't it be
xn + yn = zn, has no non-trivial solutions when n, x, y, zN, and where n ≥ 3?
Why is it acceptable to leave out nN in the formal statement?
Nick Beeson (talk) 01:51, 19 March 2016 (UTC)

It is usually assumed that n is a positive whole number and bigger than or equal to 3. — Preceding unsigned comment added by 31.53.52.160 (talk) 13:48, 2 June 2017 (UTC)

## Taniyama–Shimura-Weil conjecture history

"Around 1955, Japanese mathematicians Goro Shimura and Yutaka Taniyama suspected a link might exist between elliptic curves and modular forms, two completely different areas of mathematics. Known at the time as the Taniyama–Shimura-Weil conjecture"

Weil was 2 at that time, so how could his name have been part of the conjecture?

e: lol, whoops. Weil is André Weil, not Andrew Wiles. — Preceding unsigned comment added by 65.220.71.100 (talk) 19:29, 25 July 2016 (UTC)

To avoid having to make drastic revisions, 65.220.71.100 should take more time and study the subject carefully. — Preceding unsigned comment added by 31.53.52.2 (talk) 08:47, 22 August 2016 (UTC)

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## Solved 1965/1977?

In 1965, Dr Edward Close described the first (later) published proof (FLT65) for possibly the most famous math conjecture, ‘Fermat’s Last Theorem’ (FLT). Dr Close’s solution has, through 2016, been examined by tens of professional mathematicians including intensively over the past three years, and yet has never been refuted. Some of these experts have made suggestions or queried areas, but in every instance, further analyses by mathematicians have demonstrated the ostensible criticisms to be irrelevant to the FLT proof, or incorrect. The Close solution (FLT65), was published initially as an Appendix to Close’s Book of Atma in 1977, but remarkably, is only several pages. That contrasts with Sir Andrew Wiles’s later accepted 1994 proof of over 150 pages. [2] — Preceding unsigned comment added by 2.247.252.76 (talk) 00:11, 19 May 2017 (UTC)

A personal page issuing "press releases" is not a reliable source. This is not verifiable, and as such, not worthy of inclusion. The talk page is also not a forum for discussion about the theorem itself. If you have any specific proposal to improve the article, make it. Otherwise, this needs to be deleted because right now it amounts to little more than propaganda. Magidin (talk) 02:42, 19 May 2017 (UTC)

## Equivalent statements

In the section on equivalent statements, the connection to elliptic curves is considered an equivalent statement, although it is not: A condition is an equivalence statement when it is if and only if. The statement about Frey's curve is not such a condition because if a Frey curve could be non-modular, this would not prove the existence of a non-trivial solution for odd prime, merely its possibilty. Nxavar (talk) 08:30, 27 September 2017 (UTC)

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## "In popular culture"

My impression was that Wikipedia had decided that "In popular culture" sections should be removed, and relevant information be woven into the article. An editor added today a section In popular culture with the single reference of the Star Trek: TNG episode "The Royale". Is my impression accurate? Should this section be kept and expanded? Magidin (talk) 16:25, 26 October 2017 (UTC)

I don't think there's any strict policy on the subject. Obviously the sort of information contained in such a section can be useful, but equally I think when they move towards poorly focussed lists of all mentions in any possible TV shows they don't add value. I'd suggest leaving it in, but with very careful moderation. Mrh30 (talk) 16:31, 27 October 2017 (UTC)
I suggest that if the information helps ones understanding of the topic itself or (e.g.) its history it belongs in an appropriate part of the article, but if it shows how broadly known the topic is (or is just a pleasing or entertaining fact one would be glad to know), a Popular culture section is a good idea. I do not think we should be too po-faced about it and aim for nothing but high seriousness everywhere. In this article I think this section is fine. PJTraill (talk) 14:24, 20 February 2018 (UTC)
For me the issue is not seriousness but rather notability. I believe that the only time these pop culture references should be added is when someone has commented on the reference (reliable secondary source) and it should not be up to an editor to add something just because it is "cute". The two entries in this section currently meet this criterion so I am happy with leaving them in place if there isn't a better way to incorporate them into the article. --Bill Cherowitzo (talk) 18:47, 20 February 2018 (UTC)

## "definition at top of article is not a direct translation"

The exact translation doesn't mention integers. "Cubum autem in duos cubos, aut quadrato-quadratum in duos quadrato-quadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet" (Nagell 1951, p. 252). In translation, "It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain."98.164.67.13 (talk) 20:29, 17 February 2018 (UTC)

The definition at the top of the article and the translation in the "Fermat's conjecture" subsection are entirely different things. It is appropriate for our article to state the problem clearly and unambiguously in modern mathematical language while also later providing a translation of how Fermat originally phrased the problem. No change to our article is needed to address this. —David Eppstein (talk) 20:44, 17 February 2018 (UTC)
And besides that, this is a clear case of why context matters when you are dealing with translations (either old or modern). Fermat is clearly talking about integers and he had no need to point that out in a note that he wrote to himself. This follows from the fact that the book he wrote this marginalia in was concerned with integer solutions of polynomial equations and also the simple fact that the statement he made is so trivially false if one allows real number solutions. Bringing any of this up at the start of the article would surely be misleading and confusing. Even in the section that contains the literal translation of Fermat's words, this would be quite a red herring. --Bill Cherowitzo (talk) 21:56, 17 February 2018 (UTC)
I think your explanation should be included. The trivial fact that that FLT is false for non integers wouldn't be a red herring if handled carefully. I think people would find it interesting and illuminating to understand why FLT concerns only integers not reals. There are a number of other trivial facts about it. Such trivia could include any two numbers a+b raised to any power cannot equal c raised to the same power when a+b<c. I think that should be included since it's wording is so close to Fermat's wording. Another would be when a+b>c then a, b, c, can form a triangle whereas when a+b<c a, b, c can't. Maybe there should be a trivia section.98.164.67.13 (talk) 08:59, 18 February 2018 (UTC)

## This needs correction

Adding 3,987^12 + 4,365^12 amounts to 4,472.0000000070576171875^12,...

The values of a and b are integers. Although c is very close to an integer, it's a rational number and thus a, b, and c can all be multiplied by the same number to make all 3 of them integers. Multiply both sides of this equation by 102400000000^12 gets:

408,268,800,000,000^12 + 446,976,000,000,000^12 = 457,932,800,000,727^12

...which would still disprove the theorem. Any corrections?? Georgia guy (talk) 14:37, 15 March 2018 (UTC)

I've used an online factorization program and the numbers have 176 digits and they begin with 8503956269673, but the number on the left has a 0 as its next digit and the number on the right has a 9 as its next digit. Thus, the numbers agree to only 13 of 176 decimal digits. Any corrections?? (No, this does not violate the "this is not a forum" rule; it's related to the "In popular culture" section of this article.) Georgia guy (talk) 14:44, 15 March 2018 (UTC)

You are right, the wording of that paragraph was misleading. I have rewritten it. Gandalf61 (talk) 15:07, 15 March 2018 (UTC)

## Plain English...

The following sentence...

"In plain English, these papers by Frey, Serre and Ribet showed that if the Modularity Theorem could be proven for at least the semi-stable class of elliptic curves, a proof of Fermat's Last Theorem would also follow automatically".

...is a joke right??? Or is there some new meaning of "plain English" that I am unfamiliar with? FillsHerTease (talk) —Preceding undated comment added 20:53, 18 April 2018 (UTC)

"Plain English" refers to the sentence you have quoted, not to the papers of Frey, Serre, and Ribet. Do you find this sentence difficult to understand, in broad outline? Do you have any suggestions for how it might be rewritten to be easier to understand? —David Eppstein (talk) 23:19, 18 April 2018 (UTC)

## Inconsistency

The article on Fermat's Last theorem does not mention any proof by Gauss of the case in which n=3. — Preceding unsigned comment added by 86.166.102.132 (talk) 13:34, 11 May 2018 (UTC)

Do you have a source for Gauss having proved this? Paul August 14:15, 11 May 2018 (UTC)
The Wikipedia article on Gauss says that he proved the case in which n=3. See https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss#Career_and_achievements .
I am wondering if Gauss did actually prove this case, with n=3. — Preceding unsigned comment added by 86.166.102.132 (talk) 14:21, 11 May 2018 (UTC)
It was put in at 14:38 on 30/4/2018 by SebastianHelm. — Preceding unsigned comment added by 86.166.102.132 (talk) 14:39, 11 May 2018 (UTC)

## "In ancient times"

your recent edit restores a situation in which two sentences in close proximity begin with the phrase "In ancient times". This is just poor writing. I would be happy to discuss other ways to preserve that sense, if you think it's important, although personally I think that the more detailed discussion of the history three sentences later should be sufficient. (Also your edit is ungrammatical, but that's easy to fix.) --JBL (talk) 13:54, 6 August 2018 (UTC)

Yes, I agree that the wording was not ideal, but I don't think that justifies removing the statement altogether. The mention three sentences later is about finding sets of numbers which satisfy the equation, and does not in any way indicate a knowledge of its relation to right angled triangles. I have removed the words "in ancient times" to which you object, but left in a past tense, which I think implicitly suggests that the statement refers to the "ancient times" referred to in an earlier sentence, unlike the present tense version that you posted. I would prefer the connection to be more explicit, but I don't think it's important enough to spend a lot of effort trying to find perfect wording. The editor who uses the pseudonym "JamesBWatson" (talk) 14:07, 6 August 2018 (UTC)
Thanks -- I am happy with the way you have left it, but you are right about the later text. I will think some more about whether the connections can be made more explicit. --JBL (talk) 17:04, 6 August 2018 (UTC)

## Relevant deletion discussion

See Wikipedia:Articles for deletion/Fermat's Last Theorem in fiction (2nd nomination). XOR'easter (talk) 14:03, 11 September 2018 (UTC)

Thanks to your good works, that article seems likely to be kept. And it serves naturally as the main article for the "In popular culture" section here. Since that article is, in essence, a list, one question is how to summarize it here. I propose something like the following:

==In popular culture==

Fermat's Last Theorem has attracted notice in numerous cultural works, including in movies, theater, novels, and on television; particularly in science fiction. In one example, [put an abbreviated form of the Star Trek discussion here??]. For further examples, see Fermat's Last Theorem in fiction.

The goal is to give a sense that there are many examples, while reserving detailed discussion for the other article and making it clear that that's where one should go to find more. What do others think? --JBL (talk) 22:56, 12 September 2018 (UTC)
I think the first sentence has a lot of words but doesn't really say much. I think it's also more conventional to just link the "in fiction" article once, in the "Main" hatnote—repeating it is overkill. How about:
Fermat's Last Theorem is alluded to in many cultural works. One example is the equation ${\displaystyle 3987^{12}+4365^{12}=4472^{12}}$, which is only correct to ten significant figures, and appears in The Simpsons episode "The Wizard of Evergreen Terrace". Another is Star Trek episode "The Royale", where Captain Jean-Luc Picard laments that the theorem is still unsolved.
This is essentially what we have already, but is a bit shorter, and has the first sentence to briefly establish context. 23:06, 12 September 2018 (UTC)
I'm not too fond of the term "cultural works". How about "works of fiction" instead? Otherwise, that sounds fine to me. XOR'easter (talk) 17:00, 13 September 2018 (UTC)
Explaining a couple choices I made in the draft above:
@Bilorv: I don't care so much about the first sentence (I do think those words say something, but I know people have different writing styles and a terser approach is fine) but your subsequent sentences do something I was explicitly trying to avoid: they give two examples, stripped to the level of "here is a thing that exists." I think it would be much preferable to be really clear about where a reader can find multiple examples, and also provide enough details about one single example so that it is actually an interesting description.
the other article includes at least one example (a piece of music) that is not fiction. (I would have said that musical theater was also not fiction, although our article fiction disagrees with me.) And the section of this article is called "In popular culture". But, I don't feel strongly about this, either, if you think there's a good reason to use "fiction" instead. --JBL (talk) 11:13, 19 September 2018 (UTC)
A terser approach is not my style of writing, but a conscious choice per WP:UNDUE. This is a small aspect of a very significant topic. Multiple sentences for any example would be giving that example undue weight. "Readers would find it interesting" is not a reason to include it, unfortunately. It is standard practice to establish that the reader can learn more about the topic using {{Main}} instead of mentioning it in prose. In fact, I think that "for further examples, see..." may even be a violation of WP:SELFREF). 11:46, 19 September 2018 (UTC)
The idea that Wikipedia policies mandate that in this situation we write one sentence about two examples from a list instead of two sentences about one example is preposterous, to the extent that it is hard to know how to engage with it. If you are able/willing to discuss the actual merits of writing the sentences that describe examples one way or the other, that might be worthwhile. --JBL (talk) 15:16, 22 September 2018 (UTC)
Of course I'm willing to engage in discussion, but I can't see what reaction you expect from describing my proposal as preposterous. The example I wrote used enough detail for a reader to understand what the show's allusion was about and no more. It focused equally on the most important examples from the list, the way I saw it. Would you like to suggest alternate text that you would prefer? 18:30, 24 September 2018 (UTC)
Your proposal is not preposterous, and I did not describe it as such. (What is preposterous is the idea that any of the policies you mentioned are useful for making the choice between two or three sentences devoted to one example versus on sentence devoted to each of two or three examples.) My objection to your proposal is the following: in squeezing the two examples down to a single sentence, we end up with a (correctly referenced and supported) statement that twice FLT was mentioned on TV, but no sense at all of the significance of these mention, or why they're interesting. This is also the reason I chose Star Trek rather than the Simpsons: the two Simpsons uses are basically just throwaway jokes that don't relate to the plot or storyline, and no moral is drawn from them. The first two Star Trek sentences of the current section (including the quote, but not the parenthetical) do a much better job of showing FLT actually playing a role in a fictional work, and I would prefer to keep them over a Simpsons mention. --JBL (talk) 20:11, 24 September 2018 (UTC)
References on The Simpsons have been studied in books. The source for this particular joke is a book which discusses FLT and The Simpsons for several pages, giving it significant weight. I can't see how exactly we would explain the significance of the mentions without delving into original research; I don't believe that the current article explains significance any further (it's just more plot detail). I think we have reached an impasse, because I consider what I wrote to be both interesting and meaningful and you do not. 20:28, 24 September 2018 (UTC)
Great, if the Simpsons is the best example by some measure, then write two sentences about it that summarizes in an appropriate, encyclopedic way what the sources say about it, and get rid of Star Trek instead. --JBL (talk) 12:03, 8 October 2018 (UTC)
Granted that there is a whole other article on the topic, why do we need anything more in this article than a link to it from "See also"? Anything more than that is either redundant duplication of content in the other article or else content in this one that should be in that one and not here. The editor who uses the pseudonym "JamesBWatson" (talk) 16:21, 19 September 2018 (UTC)
Because that's how summary style works. 17:14, 19 September 2018 (UTC)
No, Wikipedia:Summary style describes how to summarise content of an article on a subtopic of the main topic, but that comes into effect only if the subsidiary article is a subtopic of the main topic. In this case, although it is clearly related, it is not a subtopic: it is not about the theorem. An analogous case is Julius Caesar, which is an article about the ancient Roman soldier and politician of that name. Julius Caesar (play), on the other hand, is not about that person, and so it does not have a summary in the article Julius Caesar. There are many other examples following the same principle: a summary section belongs in a main article on a topic if the subsidiary article is about an aspect of the topic of the main article. In this case that means that a summary section would be suitable for a secondary article if it were about an aspect of the mathematical theorem known as "Fermat's Last Theorem", but the article Fermat's Last Theorem in fiction isn't, just as the article Julius Caesar (play) isn't about the real person who is the topic of Julius Caesar. The editor who uses the pseudonym "JamesBWatson" (talk) 11:45, 20 September 2018 (UTC)
I accept that it's an edge case but I think it is a subtopic: it is about an aspect of the theorem; specifically, a part of its legacy. And the legacy of subjects is something we include in that subject's page. But I don't see WP:SUMMARY defining what a "subtopic" is; it's more about "is this a section which would normally go in this article, but is too long". Hence we get splits for things like sequels to a movie—the sequel was clearly never part of the original movie but WP:SUMMARY applies nonetheless. The nutshell template describes the splitting process which is precisely what happened to this article in 2007 in this edit. So it seems to me like WP:SUMMARY is a pretty good fit here. 12:19, 20 September 2018 (UTC)
I could go either way on it; I think the proposed rewrite by Bilorv is not valuable to any likely reader and that a See-Also link would be better, but I think that a short-but-still-readable version of the section would be worth having. --JBL (talk) 15:16, 22 September 2018 (UTC)

Does anyone who has not participated in this discussion have any comments? We seem to have reached a stalemate where none of us are happy with the current contents of the section, but no replacement has consensus. 19:05, 7 October 2018 (UTC)

Should we perhaps vote on what to do: I have created a sub-section. PJTraill (talk) 23:51, 7 October 2018 (UTC)
No, this is premature, and also not the right way to go about it (which would be to open an RfC). --JBL (talk) 12:03, 8 October 2018 (UTC)
I would not know, I am inclined to leave you to discuss further. But maybe it would help to make a list of the points at issue and discuss them one by one. For me there are at least these points (+ my opinions): should section exist (yes!)? how many examples (2!)? how much detail in examples (terse)? how many links to main (1)? What in introductory sentence (not what p~ c~ means, do say in what role FLT appears: represent v. diff problem, peg for in-jokes, &c?)? PJTraill (talk) 12:24, 8 October 2018 (UTC)
Let me be precise about why it is not necessary: obviously I have a strong view about what would make a good example, but if three other people say "we disagree, the single-sentence snippets get the point across and 2 examples is better than 1," the right thing to do would be for someone to edit the article in accordance with that consensus (that happens to have me not part of the majority view). I am not entirely convinced we have reached that point yet, but also it is not necessary to have a full RFC to get there. --JBL (talk) 12:47, 8 October 2018 (UTC)

### Voting

Anybody who cares (contributors and debaters: ), please vote for one of (or any further proposals):

• Keep – the current version as of 2018-10-08.
• Remove – remove the section and only refer in See also , as suggested by .
• New text 1 – in first post of the section by
Fermat's Last Theorem has attracted notice in numerous cultural works, including in movies, theater, novels, and on television; particularly in science fiction. In one example, [put an abbreviated form of the Star Trek discussion here??]. For further examples, see Fermat's Last Theorem in fiction.
• New text 2 – as per first reaction to JBL by @Bilorv:
Fermat's Last Theorem is alluded to in many cultural works. One example is the equation ${\displaystyle 3987^{12}+4365^{12}=4472^{12}}$, which is only correct to ten significant figures, and appears in The Simpsons episode "The Wizard of Evergreen Terrace". Another is Star Trek episode "The Royale", where Captain Jean-Luc Picard laments that the theorem is still unsolved.
PJTraill (talk) 23:51, 7 October 2018 (UTC), updated PJTraill (talk) 10:41, 8 October 2018 (UTC)
@PJTraill: tagging votes with user's names is literally "ad hominem", and semantically near. Could you, please, revise the suggested tags?
No harm meant: I do not see the tags as an attack on or invitation to attack or discuss anyone’s character as a distraction from the merits of their arguments. But since you feel that way I have changed them; unfortunately I could not think of meaningful names.

• New text 2 gets my vote. (Maybe not perfect but good enough, no point listing types of medium or repeating the link, two examples is about right.) PJTraill (talk) 23:51, 7 October 2018 (UTC)
• I suppose it's obvious that new text 2 is my preferred version, but next text 1 would be my second choice. 12:08, 8 October 2018 (UTC)
• New text 1, perhaps with some tweaks and failing that, Removal. A problem with the alternative is that in calling a non-equation an "equation", confusion is certainly introduced. A much longer explanation would be needed to set this straight and I do not see any advantage in spending more time on this coincidental curiosity. --Bill Cherowitzo (talk) 17:16, 8 October 2018 (UTC)
I feel "which is only correct to ten significant figures" clarifies it, though I concede "equation" was a bad blunder of a word choice. Would "alleged equality" or "approximation" not suffice? There's definitely a concise rewording to be found if this is your only concern. 18:56, 8 October 2018 (UTC)
I'd rather prefer a closing sentence in the lead, linking to the "fiction", just stating the popular occurrences without any examples and without a separate paragraph. But I don't really care. BTW, getting 10 digits of a 50-digit integer correct, might impress Homer, but certainly not Lisa, thinking of gravitational waves. Purgy (talk) 08:37, 9 October 2018 (UTC)
It violates MOS:LEAD to mention something in the lead and not the body. 20:09, 9 October 2018 (UTC)
"Assertion" or "claim" would do the job. PJTraill (talk) 10:18, 9 October 2018 (UTC)

## dates wrong

In this article they state that the date of Arithmetica was 1670, did they mean 1570, because further in the article says Fermat penned it in 1637. So someone has their dates wrong. 2600:387:B:5:0:0:0:B4 (talk) 07:33, 19 September 2018 (UTC)Archimedes Plutonium, 19SEP2018

You've misread the article. Diophantus wrote the Arithmetica an ancient work (c. 3rd century BC). In 1637 Fermat wrote his note in the margin of a 1621 edition of Arithmetica. A later 1670 edition of Arithmetica included Fermat's commentary. Paul August 09:26, 19 September 2018 (UTC)

Isaac Newton Institute website has a photo when Andrew Wiles prove last theorem. I would like to upload it on Wikimedia, but I don't know if it is common creative license. http://www.newton.ac.uk/event/lfnw01 — Preceding unsigned comment added by 小小地松鼠 (talkcontribs) 14:34, 22 September 2018 (UTC)

The default answer for pictures you found on the internet with no explicit declaration of a CC license is no. Asking here won't change that. You can try tracking down who actually owns the copyright on the photo (most likely either the photographer or the organization that hired the photographer), somehow persuade them to release it, and get them to communicate their explicit permission through WP:OTRS, but without that you can't upload it. —David Eppstein (talk) 17:00, 22 September 2018 (UTC)
You could start by writing to one of the addresses on their contact page, http://www.newton.ac.uk/contact. General Enquiries: Telephone: +44 (0)1223 335999 / Fax: +44(0)1223 330508 / Email: info@newton.ac.uk. Of course they may refer you to someone else, but your chances must be reasonable, given that Andre Wiles announced his proof at their institute. PJTraill (talk) 18:29, 8 October 2018 (UTC)