L and P are positive integers that satisfy this equation:

(L+1)³ – L³ = P²

For example, 8³ - 7³ = 13²; 105³ - 104³ = 181², and so on.

Prove that P is always expressible as the sum of squares of two consecutive positive integers.

(For example, 13 = 2² + 3²; 181 = 9² + 10², and so on.)

(In reply to What value for L? by brianjn)

Knowing such values does not really seem a good way to go, but if I am wrong, and it assists a resolution, so be it.

Posted by brianjn on 2008-04-09 03:44:49