# Definition:Pythagorean Triple

## Definition

A Pythagorean triple is an ordered triple of positive integers $\tuple {x, y, z}$ such that $x^2 + y^2 = z^2$.

That is, a Pythagorean triple is a solution to the Pythagorean equation.

### Primitive Pythagorean Triple

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.

## Also known as

A Pythagorean triple is also known as a (set of) Pythagorean numbers.

## Source of Name

This entry was named for Pythagoras of Samos.