I am working on the problem:
Let $m$ and $n$ be integers in the ring of integers. Show that $m\mathbb Z$ contains $n\mathbb Z$ if and only if $m$ divides $n$.
It's an if and only if proof so two directions to show. Start with the fact $n\mathbb Z$ is a subset of $m\mathbb Z$ and want to show $n=mx$ for some $x \in \mathbb Z$. Help to proceed?