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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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Hints/Tips re: need a hint Comment 7 of 7 |
(In reply to need a hint by Praneeth)

Move to:    

(2P)- 1 = 3(2L+1)     (from (2P)-3(2L+1) = 1)

Then, factorize the lhs, and ...... ......

 

Edited on July 23, 2008, 4:19 pm
  Posted by K Sengupta on 2008-07-23 16:11:47

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