Thread: pythagorean triples

prove that if x,y,z is a Pythagorean triple, than at least one of x,y,z is divisible by 5.

What I have so far: let
Then try out all of the cases. If and use congruences to show that it is true, for all of the possible values of r and s.

Is there a more elegant way to prove this, because what I have so far is too tedious.

Originally Posted by keityo

prove that if x,y,z is a Pythagorean triple, than at least one of x,y,z is divisible by 5.

What I have so far: let
Then try out all of the cases. If and use congruences to show that it is true, for all of the possible values of r and s.

Is there a more elegant way to prove this, because what I have so far is too tedious.

Consider the possible values of squares modulo , then all the possible values of modulo and which of these can a square modulo 5.

CB