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    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)...