What are the Pythagorean Triples?

A Pythagorean is a set of three integers a, b, c, which form the sides of a right triangle. The smallest set is 3, 4, and 5.

is a set of three integers a, b, c which form the sides of a right angled triangle. The smallest Pythagorean triple is the set of numbers 3,4,5. What formula do a, b, c have to satisfy for the triangle to have a right angle opposite side C?