Definition:Generator for Primitive Pythagorean Triple

Definition
The generator for a primitive Pythagorean triple is an ordered pair:
 * $G = \left({m, n}\right)$

where $m, n \in \Z$ such that:
 * $m, n \in \Z_{>0}$ are (strictly) positive integers
 * $m \perp n$, that is, $m$ and $n$ are coprime
 * $m$ and $n$ are of opposite parity
 * $m > n$.

The primitive Pythagorean triple which has been generated by $G$ is:
 * $\left({2 m n, m^2 - n^2, m^2 + n^2}\right)$

Also see

 * Solutions of Pythagorean Equation/Primitive
 * Definition:Generator for Pythagorean Triple