MathNet 2021 — Part 07 Question 100

Let $x$, $y$ and $z$ be odd positive integers such that $\gcd(x, y, z) = 1$ and the sum $x^2 + y^2 + z^2$ is divisible by $x + y + z$. Prove that $x + y + z - 2$ is not divisible by $3$.