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

Hint:

All Pythagorean triples can be written as:
$$  a = k\cdot(m^2 - n^2) ,\ \, b = k\cdot(2mn) ,\ \, c = k\cdot(m^2 + n^2),$$
where $m, n$, and $k$ are positive integers with $m \gt n, m − n$ odd, and with $m$ and $n$ coprime.
