Prove that $3a^2-1$ is never a perfect square when $a$ is an integer.
I'm not sure how to go about this proof or what form of an integer to use. I know an integer can be represented using
- $2k$, $2k+1$, or
- $3k$, $3k+1$, $3k+2$, or
$4k$, $4k+1$, $4k+2$, $4k+3$...
but how do I know which form to use for this problem?