if $\displaystyle gcd(a,n)=1$ and $\displaystyle gcd(b,n)=1$, then $\displaystyle gcd(ab,n)=1$

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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- Jun 21st 2011, 03:46 PM #1

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## if (a,n)=1 and (b,n)=1, then (ab,n)=1

if $\displaystyle gcd(a,n)=1$ and $\displaystyle gcd(b,n)=1$, then $\displaystyle gcd(ab,n)=1$

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.

- Jun 22nd 2011, 02:15 AM #2

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## Re: if (a,n)=1 and (b,n)=1, then (ab,n)=1