This question already has an answer here:
Suppose that $a,n \in \Bbb Z$ are coprime. Show that there is an integer $x$ such that $ax−1$ is divisible by $n$.
I know that $\gcd(a,n)=1$ and feel like that will be used in the proof of this, but the fact that there are no numbers is making it complicated. Do I have to work out the gcd backwards?