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Let a be an element of order n in a group and d = gcd(n,k) where...

Let a be an element of order n in a group and d = gcd(n,k) where k is a positive integer.

a) Prove that <a^k> = <a^d>

b) Prove that |a^k| = n/d

c) Use the parts you proved above to find all the cyclic subgroups and their orders when |a| = 100.

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