Pythagorean Triples

Summary. A Pythagorean triple is a set of positive integers {a,b,c} with a 2 + b 2 = c 2. We prove that every Pythagorean triple is of the form a = n 2 − m 2 b = 2mn c = n 2 + m 2 or is a multiple of such a triple. Using this characterization we show that for every n> 2 there exists a Pythagorean triple X with n ∈ X. Also we show that even the set of simplified Pythagorean triples is infinite