Question 135
Find all triples $(x, y, z)$ of positive integers such that
$$
x + y + z = 2010 \text{ and } x^2 + y^2 + z^2 - x y - y z - z x = 3.
$$
$$
x + y + z = 2010 \text{ and } x^2 + y^2 + z^2 - x y - y z - z x = 3.
$$
MathNet 2010 — Part 05 Question 135
Math Olympiad Vault · MathNet 2010 — Part 05