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Let a, b, c Z. Prove that if a|bc, then a|(a, b)c Let a, b Z and let k Z+. Prove that (ak , bk

Let a, b, c Z. Prove that if a|bc, then a|(a, b)c

Let a, b Z and let k Z+. Prove that (ak , bk ) = (a, b)k . Hint: use the prime factorizations of a, b, and (a, b)!

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