Hi, I have the following problem. I think I know how to solve the second part (I have done 2 other problems that look very similar), however, I have no clue about the first part :-/. Thanks for your help!

Part 1 (the one I have no clue about): Prove that the equation $\displaystyle x^2 \equiv 2 mod 3$ has no solution with $\displaystyle x$ in $\displaystyle \mathbb{Z}$.

Part 2 (which I think I know): Then use this to prove that the equation $\displaystyle x^2 = 2+3y$ has no solution with $\displaystyle x$ and $\displaystyle y$ in $\displaystyle \mathbb{Z}$