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dumbQuestion

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Now, it seems like Z*(n) always has some generator. But I don't want to just assume that's the case. I understand that Z*(n) is cyclic, but does every cyclic group have a generator? (or is this just part of the definition of being cyclic - that it's a group built up by some generator) Is there a theorem that says Z*(n) is cyclic? Also, how can I tell how many generators of Z*(n) there are? For example when I'm building up Dirichlet tables for Z*(n) I notice for example Z*(5) has two generators: [2] and [3], while some of the others only have a single generator. Is there any theorem that tells me exactly how many generators there are?