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

See Solutions of Pythagorean Equation.