Problem

Source: VIII International Festival of Young Mathematicians Sozopol 2017, Theme for 10-12 grade

Tags: number theory



Find all triples $(x,y,z)$, $x,y,z\in \mathbb{Z}$ for which the number 2016 can be presented as $\frac{x^2+y^2+z^2}{xy+yz+zx}$.