A set of three positive integers a, b, and c such that a2 + b2 = c2 (see Pythagoras’ Theorem). If {a,b,c} is a Pythagorean triple, then so is {ka, kb, kc} for any positive integer k. Pythagorean triples that have greatest common divisor equal to 1 include the following: {3,4,5}, {5,12,13}, {8,15,17}, {7,24,25} and {20,21,29}. A general formula for such Pythagorean triples is
where p > q are coprime, positive integers which are not both odd.