Prove $\displaystyle 3a^2 - 1$ is never a perfect square.

The book hints to use the fact: "The square of any integer is either of the form 3k or 3k+1," which we proved in a previous problem.

So how do you start?

Assuming $\displaystyle 3a^2 - 1$ is a perfect square, it must be able to be written in the form of 3k or 3k+1.

Then what? How do you show it can't or NEVER can be?