Find all triples $(x,y,z)$ of positive integers such that $$\begin{cases} x + y +z = 2010 \\x^2 + y^2 + z^2 - xy - yz - zx =3 \end{cases}$$
Problem
Source: 2010 Saudi Arabia Pre-TST 2.1
Tags: diophantine, system of equations, System, number theory
Source: 2010 Saudi Arabia Pre-TST 2.1
Tags: diophantine, system of equations, System, number theory
Find all triples $(x,y,z)$ of positive integers such that $$\begin{cases} x + y +z = 2010 \\x^2 + y^2 + z^2 - xy - yz - zx =3 \end{cases}$$