Definition:Pythagorean Triple/Primitive/Canonical Form

Definition
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.

Also see

 * Parity of Smaller Elements of Primitive Pythagorean Triple which shows that $x$ and $y$ can not both be odd or both be even.

Hence $z$ must also be odd.


 * Elements of Primitive Pythagorean Triple are Pairwise Coprime