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

Source of Name

This entry was named for Pythagoras of Samos.