Obtain the following version of the Division Algorithm : For integers a and b, with b ≠ 0, there exist unique integers q and r that satisfy a = qb + r, where .
[Hint: First write a = q′b + r′, where 0<r′<|b|. When , let r = r′ and q = q′; when , let r = r′ − |b| and q=q′+l if b > 0 or q = q′− 1 if b<0.]
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