if and , then I believe this is true but not sure on how to prove it. I tried Bezout's identity, but I couldn't see what to do next or it just didn't go anywhere.

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Originally Posted by dwsmith if and , then I believe this is true but not sure on how to prove it. I tried Bezout's identity, but I couldn't see what to do next or it just didn't go anywhere. Let gcd(a,n)=1 and gcd(b,n)=1 and suppose that gcd(ab,n)=N>1. Let p be a prime divisor of N, then p|ab and p|n. But p|ab implies p|a or p|b which is a contradiction. Therefore gcd(ab,n)=1. CB