What I know is that I should prove $\forall \bar{x}\in \mathbb{Z}/3\mathbb{Z}$ , $\exists n\in \mathbb{Z}$ (non-zero) such that $n\bar{x}=0$
How can I do it ?
$\bar{x}$ can only be $\bar{0}$ , $\bar{1}$ , or $\bar{2}$ , right ?
So if I choose $n=3y$ where y is an integer , will it be helpful ?