Thread: Need helpful hints

Hey everyone. If anyone could point me towards a hint on the following problem I would greatly appreciate it.

Let n and m be positive integers, with n > m ≥ 2. Describe as completely as you can the possible ring homomorphisms from Zn to Zm. Under what conditions on n and n will there be nontrivial homomorphisms? Under what conditions on n and m will there be surjective homomorphisms?

Start by looking at a couple of simple examples. What are the possible homomorphisms from to ? What about to ? What about to or ?