> 
> Define the map
>  $f : \Bbb Z/6\Bbb Z\to\Bbb Z/3\Bbb Z \times\Bbb Z/2\Bbb Z$
>  by
>  $f([a]\_6) = ([a]\_3, [a]\_2)$
>  where $[a]\_n$ denotes the residue class of $a \in\Bbb Z$ modulo $n$. Prove that $f$ is an isomorohism.
>  Try to prove that if $\gcd(m, n) = 1$, then the groups $\Bbb Z/mn\Bbb Z$ and $\Bbb Z/m\Bbb Z\times\Bbb Z/n\Bbb Z$ are
>  isomorphic.
> 
> 
> 

Can anyone help with this question?

I have prove only that $\gcd(m,n)=1$.