1 Euclid's Division Lemma We consider a couple of extensions of Euclid's division lemma We have already seen how to make it work when a is any integer and b is a positive integer What about if we only assume that b 0 Prove that for any integer a and any non zero integer b , there exist unique integers q,r such that a bq r and 0 1 Euclid's Division Lemma We consider a couple of extensions of Euclid's division lemma We have already seen how to make it work when a is any integer and b is a positive integer What about if we only assume that b 0 1 Prove that for any integer a and any non zero integer b, there exist unique integers q,r such that a bq r and 0r

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1 Euclid's Division Lemma  We consider a couple of extensions of Euclid's division lemma  We have already seen how to make it work when a is any integer and b is a positive integer  What about if we only assume that b  0    Prove that for any integer a and any non zero integer b , there exist unique integers q,r such that a bq r and 0   1 Euclid's Division Lemma We consider a couple of extensions of Euclid's division lemma  We have already seen how to make it work when a is any integer and b is a positive integer  What about if we only assume that b 0   1  Prove that for any integer a and any non zero integer b, there exist unique integers q,r such that a bq r and 0r

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1 Euclid's Division Lemma We consider a couple of extensions of Euclid's division lemma. We have already seen how to make it work when a

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