Given the function $f: \frac{\mathbb Z}{mn\mathbb Z} \rightarrow \frac{\mathbb Z}{m\mathbb Z} \times \frac{\mathbb Z}{n\mathbb Z}$ defined by $f([a]_{mn}) = ([a]_m, [a]_n)$.
I must:
Show that $f$ is well-defined.
Show that if $m=6$ and $n=10$ that $f$ is neither injective nor surjective.
Show in general that if $m,n$ have a common divisor $d>1$, then $f$ is neither injective nor surjective.