# Definition:Pythagorean Equation

## Definition

The Pythagorean equation is the Diophantine equation:

$x^2 + y^2 = z^2$

where $x, y, z$ are integers such that $x, y, z > 0$.

Solutions of this equation are known as Pythagorean triples.

If, in addition, $\left({x, y, z}\right)$ is a primitive Pythagorean triple, then $\left({x, y, z}\right)$ is known as a primitive solution of $x^2 + y^2 = z^2$.

## Source of Name

This entry was named for Pythagoras of Samos.