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.
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)...