\begin{definition}[Definition:Generator for Primitive Pythagorean Triple]
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:
:$\left({2 m n, m^2 - n^2, m^2 + n^2}\right)$
\end{definition}