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