2. Are there integers a, b and c (all non-zero) such that a|bc but a/|b and a/|c?
3. Let a, b, c be integers. Prove the following statement: If ac divides bc and c ≠ 0, then a divides b.
4. Let a, b and c be integers. Prove that if a divides b and a does not divide c then a does not divide b + c.
5. Using the Euclidean Algorithm ﬁnd the gcd(a, b) and write the gcd(a, b) in the form ax + by, where x, y ∈ Z (show your work!)
(a) a = 3953 and b = 944
(b) a = 4653 and b = 1324
(c) a = 5280, b = 3600
(d) a = 19200 and b = 3587
6. Let a, b and d be positive integers.
(a) Show that d gcd(a, b) divides both ad and bd
(b) Prove that gcd(ad, bd) = d gcd(a, b).
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