Thread: cyclic group of order m

If G=<a> is a cyclic group of order m generated by an element a∈G, then for each divisor r of m exhibit explicitly an element c∈G of order r.

Have you even tried this? This really isn't too hard. It doesn't even ask you to show that the element you find with order $\displaystyle r$ is unique. If $\displaystyle r|m$ what can we say about $\displaystyle a^{\frac{m}{r}}$?