TITLE: Why can't prime numbers satisfy the Pythagoras Theorem? That is, why can't a set of 3 prime numbers be a Pythagorean triplet?
QUESTION [16 upvotes]: Suppose $a$, $b$ and $c$ are three prime numbers. 
How to prove that $a^2 + b^2 \neq c^2$?

REPLY [2 votes]: because one of them must be even number.