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Equality of gcd's

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Show that if gcd(a, b) = 1, then gcd(ac, b) =gcd(b, c).

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Solution Summary

This solution is comprised of a detailed explanation to show that if gcd(a, b) = 1, then gcd(ac, b) =gcd(b, c).

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Proof:
Let x=gcd(ac,b), y=gcd(b,c).
First, since y=gcd(b,c), then y|b, y|c, so y|ac, thus y is a ...

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