Find all triples $(x,y, z)$ of integers such that $$\begin{cases} x^2y + y^2z + z^2x= 2010^2 \\ xy^2 + yz^2 + zx^2= -2010 \end{cases}$$
Problem
Source: 2010 Saudi Arabia BMO TST 3.4 - Balkan Math Olympiad
Tags: system of equations, System, diophantine, number theory