> 
> I'm trying to proof that 
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> 
> $$(ℤ/mℤ)/(\bar n) ≅ℤ/nℤ$$
> 
> 
> with $n|m$.
> 
> 
> 

A $m=kn$, we have that:

$$ℤ/mℤ=\{\bar 0,...,\bar n,...,\overline {c(n-1)}\}$$

If the equality: $\bar n = \bar 0$ holds, then obviously we can write this set as:

$$\{\bar 0, \bar 1 ,...,\overline{n-1}\}$$

Some part of me says, this is completely trivial, this is the proof, but an other part of me says I need to show a lot more to make this rigorous. Which part is right ?