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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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Comments: ( Back to comment list | You must be logged in to post comments.)
re: What value for L? | Comment 3 of 7 |
(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

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