1. The problem statement, all variables and given/known data Let G be a finite cyclic group of order n. Let a be a generator. Let r be an integer, not zero, and relatively prime to n. a)Show that a^r is also a generator of G. 2. Relevant equations 3. The attempt at a solution For the first one I need to show that for any element b in G there exists some integer m s.t. (a^r)^m = b. I have no idea what to do. The great thing about this is that I will be tested on this tomorrow. Ha, you get it. Pleast try to answer as soon as possible. Thanks for any help.