Let a, b, c, d be strictly positive integers. Prove the following:
(a) If a|b and b|c and gcd(a, c) = 1, then we must have a = 1.
(b) If a|c, b|c and gcd(a, b) = d, then ab|cd.
[Hint: Bézout is helpful.]
(c) If gcd(a, c) = 1 and gcd(b, c) = d, then gcd(ab, c) = d.
[Hint: what can you say about numbers which divide both ab and c
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