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  1. B

    Proving the number of solutions to |a|+|b|= k

    Yes--I see how Case 2 fits in conceptually at least. I'm thinking about it as k=0 + 1 + 1 + \cdots + 1 + 0 and then the same argument for gaps between 1s, but for the gaps between a zero and a one, there are only 2 solutions (a, 0) and (-a, 0) for the 0+1+... gap and (0, -a) and (0, a) for the...
  2. B

    Proving the number of solutions to |a|+|b|= k

    Homework Statement Prove that there are 4k solutions to the equation |a|+|b| = k, i.e. 4k pairs of a and b such that |a|+|b|=k. Homework Equations none The Attempt at a Solution I've written out the first few: for k = 0, the only solution is (0,0) for k =1, we have (-1,0) (0, -1) (0,1)(1,0)...
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