Wikipedia:Reference desk/Archives/Mathematics/2012 September 24

= September 24 =

something in Pythagoras tree (fractal)
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)


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

Bubba73 You talkin' to me? 03:22, 24 September 2012 (UTC)

Parity of elements of a pythagorean triple
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)


 * 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)
 * 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)