integer right triangles

[vanLudwig]

Look at Wikipedia for Pythagorean Triples:

Euclid's formula is a fundamental formula for generating Pythagorean triples given an arbitrary pair of integers m and n with m > n > 0. The formula states that the integers
$$a=m^{2}-n^{2}, b=2mn, c=m^{2}+n^{2}$$
form a Pythagorean triple. The triple generated by Euclid's formula is primitive if and only if m and n are coprime and not both odd.