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 Does this explain why 7 is a factor of n? by broll)

Unfortunately it does not.

In steps 3 and 4 all you really did was introduce variables k and l (the x and y seem irrelevant.)

In steps 5 and 6 you prove that (k+l) is divisible by 7.  For instance if n=3, (k+l)=21.

Posted by Jer on 2010-04-06 10:18:02