Definition:Pythagorean Triple/Primitive

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Definition

Let $\tuple {x, y, z}$ be a Pythagorean triple such that $x \perp y$ (that is, $x$ and $y$ are coprime).

Then $\tuple {x, y, z}$ is a primitive Pythagorean triple.


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.


Also see


Source of Name

This entry was named for Pythagoras of Samos.


Sources