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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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  Subject Author Date
Hints/Tipsre: need a hintK Sengupta2008-07-23 16:11:47
need a hintPraneeth2008-07-23 03:40:32
Some Thoughts AND the n-th member is:Ady TZIDON2008-04-10 17:01:24
re: What value for L?Brian Smith2008-04-10 00:15:01
re: What value for L?brianjn2008-04-09 03:44:49
What value for L?brianjn2008-04-09 03:36:06
Some Thoughtsfirst thoughtsFrankM2008-04-08 22:58:08
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