(a) Find all generators of the cyclic groups (Z12, +), (Z16, +), and (Z24, +). (b) Let...

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(a) Find all generators of the cyclic groups (Z12, +), (Z16, +), and (Z24, +).
(b) Let G = (a) with σ(a) = n. Prove that ak, k ∈ Z+, generates G if and only if k and n are relatively prime.
(c) If G is a cyclic group of order n, how many distinct generators does it have?
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