Solutions of Pythagorean Equation/Primitive

Theorem
The set of all primitive Pythagorean triples is generated by:
 * $\tuple {2 m n, m^2 - n^2, m^2 + n^2}$

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