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Let |a| = n. Prove that <a^i> = <a^j> if and only if gcd(n,i) = gcd...

Let |a| = n. Prove that <a^i> = <a^j> if and only if gcd(n,i) = gcd (n,j) and |a^i| = |a^j| if and only if gcd(n,i) = gcd(n,j).

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