For n ≥ 1, and positive integers a, b, show the following:
(a) If gcd(a, b)= 1, then gcd(an, bn) = 1.
[Hint: See Problem 20(a), Section 2.2.]
(b) The relation an |bn implies that a | b.
[Hint: Put d = gcd(a, b) and write a = rd, b = sd, where gcd(r, s) = 1. By part (a), gcd(rn, sn) = 1. Show that r = 1, whence a = d.]
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