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.

The third value I find which satisfies the conditions is:

2118480 (=37830 * 56)

6355441 (= 3*2118480 + 1 = 2521 squared)

8473921 (= 4*2118480 + 1 = 2911 squared)

Tested N up to 10,000,000

 

Posted by ed bottemiller on 2010-04-01 16:06:15