P is a positive integer such that each of 2P + 1 and 3P + 1 is a perfect square.

Prove that P is divisible by 40

Given 2P and 3P and division by 40 two values are immediately clear, 80 and 120 yielding perfect squares of 81 and 121.

... but the proof?

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I have also found that 3960 satisfies this:
             2 * 3960 + 1 =  7981      [89*89]
  and      3 * 3960 + 1 = 11881     [109 * 109]

The next occurrence seems to be;
            2 * 388080 +1 =   776161 [881 * 881]
            3 * 388080 +1 = 1164241 [1079*1079]

Edited on May 13, 2008, 10:48 pm

Posted by brianjn on 2008-05-13 22:05:02