Let a, b, and c be natural numbers and gcd(a, b) = d. Prove that
(a) a divides b if and only if d = a.
(b) if a divides bc and d = 1, then a divides c.
(c) if c divides a and c divides b, then particular,
(d) for every natural number n, gcd(an, bn) = dn.
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