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Curious Consecutive Conundrum (Posted on 2008-04-08) Difficulty: 4 of 5
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.)

See The Solution Submitted by K Sengupta    
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Some Thoughts AND the n-th member is: | Comment 5 of 7 |

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
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