Find all triples of integers $(x, y, z)$ not zero and relative primes in pairs such that $\frac{(y+z-x)^2}{4x}$, $\frac{(z+x-y)^2}{4y}$ and $\frac{(x+y-z)^2}{4z}$ are all integers.
Problem
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2015 C2 p4
Tags: number theory, Integers