Primitive Pythagorean Triples

Primitive Pythagorean Triples {x,y,z} can be generated by two positive integers a and b. x = 2ab y = a^2 - b^2 z = a^2 + b^2 as long as ... (1) b < a (2) a and b have opposite parity (3) a and b are relatively prime (GCD=1)