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teleport
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Homework Statement
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.
Homework Equations
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.