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Produce More (Posted on 2012-05-29) Difficulty: 2 of 5
Among pairs of numbers whose sum is 16, 8*8=64 is the greatest possible product. However, if we allow for a sum of 17 then there are 3 distinct ways of achieving a higher product with two positive integers: 9*8, 10*7, and 11*6 are all greater than 64.

Among pairs of numbers whose sum is 2n, n*n=n2 is the greatest possible product. However, if we allow for a sum of 2n+1 then there are 2012 distinct ways of achieving a higher product with two positive integers.

Find the minimum value of n.

No Solution Yet Submitted by Jer    
Rating: 5.0000 (1 votes)

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Possible solution | Comment 1 of 5

 If m=2012, and 2n+1 = 2m^2-2m+3, then n = 4046133.

Quite hard for D2.


  Posted by broll on 2012-05-29 11:53:19
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