|WikiProject Mathematics||(Rated B-class, Mid-priority)|
|This is the talk page for discussing improvements to the Euler's theorem article.|
Math investigatory project
- Such a statement has now been removed from the article.--Leif edling (talk) 06:17, 18 May 2009 (UTC)
I was taught that Euler's Theorem stated, that, in solids, the number of faces (F) plus the number of vertices (V)equals the number of edges (E) plus two. Is that not Euler's Theorem? —Preceding unsigned comment added by 22.214.171.124 (talk) 00:33, 29 May 2009 (UTC)
- There are many mathematical results named after Euler. The one you mention is sometimes called Euler's formula, and is generalised in the Euler characteristic. Gandalf61 (talk) 09:52, 29 May 2009 (UTC)
This theorem is stated as an implication: if a and n are coprime, then we know that the value is 1. That's the way the theorem is stated here and in most textbooks (I just checked Fundamental number theory with applications by Richard A. Mollin, page 93). This is the non-trivial result.
The converse is true, but it's so trivial that it does not have to be stated. An equivalent form of the converse is: if a and n are not coprime, then we know that the value is not 1. This is obvious: Let p be any prime that divides both a and n, then for all positive integers x we know that p divides , hence this value is not 1.
- I completely agree. The article must give a statement of the theorem as it appears in most reliable sources, which is as a one-way implication. I don't mind whether we also mention the converse or not - as Misof says, it is trivially true. But we must not change the statement of the original theorem. Gandalf61 (talk) 09:15, 18 March 2011 (UTC)
History of Euler's theorem
The article states that Euler's theorem was first proved in 1736. That can't be correct because according to Wikipedia's article "Euler's totient function", φ (n) was not defined by Euler until 1760. What Euler proved in 1736 was Fermat's little theorem. (As usual, Fermat presented the theorem but not its proof.) Even in 1760, Euler did not use the symbol φ (n) for the totient function; Gauss did that later. Also, Euler didn't call φ (n) "the totient function"; instead, he called it "numerus partium ad N primarum" (i.e., the number of parts prime to N -- or the number of natural numbers that are smaller than N and relatively prime to N). Euler's proof of "Euler's theorem" first appeared in print in 1763. I'll make appropriate changes to the article. Cwkmail (talk) 19:29, 20 December 2012 (UTC)