# Definition:Generator for Pythagorean Triple

## Definition

Let $P = \left\{ {a, b, c}\right\}$ be a Pythagorean triple

A generator for $P$ is an ordered pair:

$G = \left({m, n}\right)$

where $m, n \in \Z$ such that:

$a = 2 m n$
$b = m^2 - n^2$
$c = m^2 + n^2$