Prove 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 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?
Ok, so by showing that there's no possible way to put it into the form would be like "let a=2s+1" ... ect ... which is not of the form 3k or 2k+1 and so on with "let a+2s" ... ? Is that enough?
But wait: how do we even know a is an integer at all? The problem never said so ... ?