TITLE: Pythagorean triples and perfect squares
QUESTION [6 upvotes]: This problem is giving me difficulty:

Show that in any Pythagorean triple there exist at most a single perfect square

So far I've been working with the equations for primitive Pythagorean Triples (ie $x = m^2 - n^2$, $y = 2mn$, $z = m^2 + n^2$) but that hasn't really worked out and the problem doesn't necessarily require the triples to be primitive, so I'm stuck here. I will appreciate any help.

REPLY [4 votes]: Pretty neat effort by Warren. Well, if you have two or more pythagorean triplets to be squares you get trivial diophantine with no solutions. They are: 
$r^2+s^4=t^4$ and $r^4+s^4
=t^2$.