If 2n2 + 1 or 2n2 - 1 is a perfect square say m2 = 2n2 + 1 or 2n2 - 1 then prove that (mn)2 is a triangular number.
I tried solving for m2 or n2 and tried to bring it to the required form for a triangular number, but alas was unable to do so. However, i also realised that m is odd and tried to substitute m as 2l + 1 for some l and tried solving which didn't help as well. I have verified this for m = 3 and n=2 which in turn gives mn = 6 and in turn (mn)2 = 36which indeed is a triangular number.
I have no idea about Pell's equation as I have seen several problems on triangular numbers being solved by Pell's equation. All the topics in which I can consider myself to have sufficient knowledge include Modular arithmetic, properties of triangular number and other basic stuff such as induction,etc..
Thanks in advance!!!