Let $n \geq 2$, and let $G = \mathbb{Z}/n\mathbb{Z}$, which is a group under addition. There is a function $\phi_{\bar{a}}(\bar{x}):G \rightarrow G$ for every $\bar{a} \in G$, with $\phi_{\bar{a}}(\bar{x})=\bar{a} \cdot \bar{x}$.
Now I'm asked to prove that every homomorphism $\psi: G\rightarrow G$ equals some $\phi_{\bar{a}}$. I've already established $\phi_{\bar{a}}$ is a homomorphism.
Since $\psi$ is a homomorphism I know that $\psi(\bar{x}+\bar{y})=\psi(\bar{x})+\psi(\bar{y})$ but I have no idea how to tie this to $\phi_{\bar{a}}$. Any suggestions?
Hint: Given a homomorphism $f:G\to G$ write $\bar{a}=f(1)$. Now use the properties of a homomorphism.