If $\gcd(n,a)=1$, and $\gcd(n,b)=1$ prove $\gcd(n,ab)=1$

Question

If $\gcd(n,a)=1$, and $\gcd(n,b)=1$, prove $\gcd(n,ab)=1$

Hey. What are your own thoughts on this problem, and where are you stuck? — Mankind, Mar 14 '16 at 19:24
I'm not sure how to prove this. Even my professor said that he didn't know how to. — Cantwait428, Mar 14 '16 at 19:25

score 1 · Answer 1 · answered Mar 14 '16 at 19:24

1

Hint: $ua+vn =1, u'b+v'n=1$. $(ua+vn)(u'b+v'n)=1 = uu'(ab)+(uav'+u'vb+vnv')n$

answered Mar 14 '16 at 19:24

Tsemo Aristide

1 Answers1