Proof regarding multiples of 3

Question

Let $a = x^2 + y^2 + z^2$ for $a, x, y, z \in \mathbb{Z_{>0}}$. I'm trying to prove that if $a$ is divisible by 3, then $x, y, z$ are either ALL divisible by 3, or NONE of them are divisible by 3.

I am not sure where to start. I wrote down the definition, $\exists w \in \mathbb{Z_{>0}}$ such that $a = 3w$, but from there I am lost. I also know that if $x$ is divisible by 3 then so is $x^2$ but am not sure how to work that in here.

Answer 1

Hint

$x^2$ is equal either to $0$ or to $1$ modulo $3$.