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Integer Forms (Posted on 2012-01-07) Difficulty: 2 of 5
Let us denote F(n) = Σi= 1 to n i*(-1)i+1

For example, F(4) = 1-2+3-4, F(5) = 1-2+3-4+5, F(6) = 1-2+3-4+5-6... 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    
Rating: 4.0000 (1 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Solutionre: Some Observations (partial solution) / The restJer2012-01-07 20:29:52
Some Observations (partial solution)Dustin2012-01-07 18:21:48
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