Hi again, another question I am having trouble starting:

Let $\displaystyle I$ be a nonempty subset of $\displaystyle \mathbb{Z}$ such that:

$\displaystyle (\forall x \in I)(\forall y \in I)[(x-y) \in I]$ and $\displaystyle (\forall z \in \mathbb{Z})(\forall x \in I)[z \cdot x \in I]$.

Show that for some $\displaystyle n \in I, I = \{z \in \mathbb{Z} \colon z = xn \ for \ some \ x \in \mathbb{Z}\}$.

Please no full solutions, but if someone could show me how to proceed