# 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

Hence $z$ must also be odd.

## Source of Name

This entry was named for Pythagoras of Samos.