Pythagorean triple/Definition

Pythagorean triple

A Pythagorean triple is an integral solution ${}(x,y,z)\in \mathbb {Z} ^{3}$ of the Diophantine equation

${}x^{2}+y^{2}=z^{2}\,.$

It is called primitive if ${}x,y,z$ do not have a common factor ${}\neq 1$.