N is a positive integer such that each of 3*N + 1 and 4*N + 1 is a perfect square.

Is N always divisible by 56?

If so, prove it. Otherwise, give a counterexample.

(In reply to re: Does this explain why 7 is a factor of n? by Jer)

You're quite right. I should have said only that either both k and l are divisible by 7, or neither are.

I was thinking mainly in terms of the earlier comments on modular arithmetic, given the additional identity n=k-l, and some surmises of my own about squares that are the sum of consecutive squares while also being the difference between consecutive cubes.

I'll try not to wander in future!

Posted by broll on 2010-04-06 15:32:36