How do I answer this?
Prove that it is impossible to find any integer $n$ such that $n^2 \equiv 2 \pmod 4$ or $n^2 \equiv 3 \pmod 4$. Hence or otherwise, prove that there do not exist integers $m$ and $n$ such that $3m^2 - 1 = n^2$.
I'm still stuck :(
Regarding to "what is n^2 congruent to each of the 0,1,2,3 cases, is it just 0,1,4,9? What do I do next?