Let G be a finite cyclic group of order n. Let a be a generator. Let r
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Question:
Let G be a finite cyclic group of order n. Let a be a generator. Let r be an integer not 0, and relatively prime to n.
(a) Show that ar is also a generator of G.
(b) Show that every generator of G can be written in this form.
(c) Let p be a prime number, and G a cyclic group of order p. How many generators does G have?
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