Prove if |a| = n in a group, then ⟨a^k⟩ = ⟨a^gcd(n,k)⟩ and |a^k| = n / gcd(n/k) (ILIEKMATHPHYSICS)

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{a^k}={a^gcd(n,k)} and |a^k|=n/gcd(n,k){a^k}={a^gcd(n,k)} and |a^k|=n/gcd(n,k)
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