\begin{definition}[Definition:Pythagorean Equation]
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 $x^2 + y^2 = z^2$.
\end{definition}