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7:05 AM
Should one of these two questions be closed as a duplicate? Which one should be left open?
Q: If gcd (a,b)=1 and gcd (a,c)=1, then gcd (a,bc)=1

LilHow do I go about proving this? If gcd (a,b)=1 and gcd (a,c)=1, then gcd (a,bc)=1. I'm very confused with gcd proofs.

Q: Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$

Suzanne FrankShow that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$. I am new at proofs and I think I should use Euclid's Lemma which states "If $p$ is a prime that divides $ab$, then $p$ divides $a$ or $p$ divides $b$. However, I am not sure how to create a concrete proof or argument. Any ...

The newer question asks for equivalence, but one direction is, in my opinion, easy.
The older question has more answers.

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