If n is a positive integer, then will denote the cyclic group of order n.
If , prove that .
There is a known result which says if is cyclic group of order then is isomorphic to (or in your notation ). To show that is isomorphic to it is sufficient to show (which is immediate) and also that is cyclic. Thus, we need to find a generator. Show that has order and therefore it must generate the whole group. This will show the group is cyclic and complete the proof.