# Pythagorean triple

• May 18th 2009, 03:05 PM
cathwelch
Pythagorean triple
Prove that in a primitive Pythagorean triple x, y, z, the product xy is divisible by 12, hence 60|xyz.
• May 18th 2009, 09:58 PM
Isomorphism
Quote:

Originally Posted by cathwelch
Prove that in a primitive Pythagorean triple x, y, z, the product xy is divisible by 12, hence 60|xyz.

Try to use the following results:
Any pythogorean triple is of the form $x = m^2 - n^2, y = 2mn$ and $z = m^2 + n^2$ where m and n are of different parity.