Prove that the number $6n+2$ is not a square for any integer $n$

Question

Prove, if $n \in \mathbb{N}, b \in \mathbb{Z}$ then $\left( 6n+2\right) \neq b ^{2}$.

Just give me a hint. I've been trying to solve it for over na hour.

Answer 1

$$ 0^2\equiv 0\\ 1^2\equiv 1\\ 2^2\equiv 4\\ 3^2\equiv 3\\ 4^2\equiv 4\\ 5^2\equiv 1\\ $$ modulo $6$. So $2$ is not a quadratic residue mod $6$.

Answer 2

Hint: What remainders $\mod 6$ can have squares of integers?