Describe all group homomorphisms $\displaystyle f: \mathbb{Z} \ \rightarrow \ \mathbb{Z} $. Give their kernels and state which are injective and which are surjective.
Its probably a really obvious solution, but I just can't think how to PROVE this. Its really annoying, I'm no good at this branch of mathematics and I need to be walked through. I'm not as mathematically inclined as the majority of other members on this site and I really need help.