Definition:Pythagorean Triple/Primitive

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

Then $\left({x, y, z}\right)$ is a primitive Pythagorean triple.

Also see

 * Parity of Elements of Primitive Pythagorean Triple which shows that $x$ and $y$ can not both be odd or both be even.


 * Elements of Primitive Pythagorean Triple are Pairwise Coprime