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September 24[edit]

something in Pythagoras tree (fractal)[edit]

In Pythagoras tree (fractal) there is "box of size 6L × 4L>." Does the ">" mean anything or is it a typo? (There is another one later.) Bubba73 ^{You talkin' to me?} 01:55, 24 September 2012 (UTC)[reply]

Just a typo. It was accidentally introduced when a reference was added: see [1]. —Bkell (talk) 02:22, 24 September 2012 (UTC)[reply]

Resolved

Bubba73 ^{You talkin' to me?} 03:22, 24 September 2012 (UTC)[reply]

Parity of elements of a pythagorean triple[edit]

Hello.

I'm having trouble with arriving to a proof that, if a, b and c are pythagorean triples without a common factor (a = p² - q², b = 2pq and c = p² + q²) then exactly one of a, b must be even and the other odd.

Any help is appreciated.186.28.123.46 (talk) 16:04, 24 September 2012 (UTC)[reply]

Clearly b = 2pq is even. If a is also even, what is the parity of c² ? So what is the parity of c ? So what factor do a, b and c have in common ? Gandalf61 (talk) 16:12, 24 September 2012 (UTC)[reply]

If both a,b are odd, then a²,b² have a remainder of 1 when divided by 4, and so a²+b²=c² has a remainder of 2 when divided by 4, but it is impossible for a square number. Therefore, at least one of a,b is even. --84.229.150.202 (talk) 18:48, 24 September 2012 (UTC)[reply]