Definition:Pythagorean Triple/Primitive

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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 known as

A primitive Pythagorean triple is also known as a primitive solution of $x^2 + y^2 = z^2$.

Also see

Source of Name

This entry was named for Pythagoras of Samos.