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=n^{2} 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.
If m=2012, and 2n+1 = 2m^22m+3, then n = 4046133.
Quite hard for D2.

Posted by broll
on 20120529 11:53:19 