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.)

Proof-no   Recursive formula-yes

a(1)=7

a(2)=104     and for the following (n>=3) members:

a(n) = 14a(n-1) - a(n-2) + 6.

Posted by Ady TZIDON on 2008-04-10 17:01:24