\begin{definition}[Definition:Pythagorean Triple/Primitive/Canonical Form]
Let $\tuple {x, y, z}$ be a primitive Pythagorean triple.
The convention for representing $\tuple {x, y, z}$ as a (primitive) Pythagorean triple is that $x$ is the even element, while $y$ and $z$ are both odd.
This is the '''canonical form''' of a Pythagorean triple.
\end{definition}