\begin{definition}[Definition:Generator for Pythagorean Triple]
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:
: $a = 2 m n$
: $b = m^2 - n^2$
: $c = m^2 + n^2$
\end{definition}