Prove that 3n^2 - 1 can't be a square of a integer n

[walker242]

Well, the problem statement is in the title:
Given that n is an integer, show that 3n² - 1 can't be the square of an integer.

Currently, I don't have any idea at all where to start. Method is probably to assume opposite and show that this leads to a contradiction.

Any hint as to where to start would be very appreciated!

 

[Dick]

Look at remainders mod 4. What are the possible values for n^2 mod 4?

 

[walker242]

Thanks for the reply!

While that probably is one way of looking at the problem, we haven't yet reached modulus in our studies.

 

[Dick]

You don't really need to study modulus to think about remainders after division by 4. Nothing else comes to mind as an approach.