Pythagorean triple ($a^2+b^2=c^2$)

A Pythagorean triple consists of three positive integers satisfying $x^2+y^2=z^2$. It is primitive when their greatest common divisor is one. Reducing their square numbers modulo $3$ shows that at least one leg is divisible by $3$; reducing modulo $4$ shows that both legs cannot be odd.

A Pythagorean triple consists of three positive integers \(a\), \(b\), and \(c\) that satisfy the equation \[ a^2 + b^2 = c^2 \] In this equation, \(c\) represents the length of the hypotenuse of a right triangle, while \(a\) and \(b\) are the lengths of the other two sides.