If $\gcd(a, c) = 1$ and $b \mid c$, prove that $(a, b) = 1$
-Not sure how to approach this problem.
-We have just started the greatest common divisor section, and looking at my notes I see that $(a \mid c = 1) \implies ax+by = 1$, would this be useful?
-My train of thought is $b \mid c$ then this proof would be relatively straight forward since $c$ is a multiple of $b$.
-I'm struggling with how I would set this up as a proof, any help is appreciated.