# Math Help - Prove that the equation x^2 equivalent tio 2 mod 3 has no solution with x in Z.

1. ## Prove that the equation x^2 equivalent tio 2 mod 3 has no solution with x in Z.

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

2. Hint: Consider all possible remainders when x is divided by 3.