Definition:Pythagorean Triple/Primitive

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.

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

Also see

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


 * Elements of Primitive Pythagorean Triple are Pairwise Coprime