Given $\displaystyle f$, natural mapping from $\displaystyle \mathbb{Z} \text{ to }\mathbb{Z}_n\text{ with }f(m)=r$, where $\displaystyle r$ be the remainder if $\displaystyle m$ is divided by $\displaystyle n$.

Show that $\displaystyle f$ is homomorphism!

And determine $\displaystyle ker(f)$.

Is $\displaystyle f$ monomorphism?