# 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:

$\left({2 m n, m^2 - n^2, m^2 + n^2}\right)$