
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 $\displaystyle Z_3$ to $\displaystyle Z_2$? What about $\displaystyle Z_4$ to $\displaystyle Z_2$? What about $\displaystyle Z_6$ to $\displaystyle Z_2$ or $\displaystyle Z_3$?