Let's first recall some Pythagorean Triples :

$\displaystyle (3,4,5) ~,~ (5,12,13) ~,~ (8,15,17) ~,~ (9,40,41) ~,~ (11,60,61) $ etc .

Can you see a pattern ? In every triple , we must find one integer from $\displaystyle (x,y,z) $ , such that it is the mutiple of $\displaystyle 5 $ .

$\displaystyle 5,5,15,40,60$ etc .

I would like you to prove this fact , the proof shouldn't be so long , i believe ...