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Integer Forms (Posted on 20120107) 

Let us denote F(n) = Σ_{i= 1 to n} i*(1)^{i+1}
For example, F(4) = 12+34, F(5) = 12+34+5, F(6) = 12+34+56... and, so on.
(1) Determine the general form of two positive integers x and y that satisfy:
F(x) + F(y) + F(x+y) = 2012
(2) Can you explain why no positive integer solution exists whenever F(x) + F(y) + F(x+y) = 2011?
No Solution Yet

Submitted by K Sengupta

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