2πik Problem 5. Let n ≤ Z be fixed. Given k Є Z+, let zk = e²²= C. This is an element of the group of n-th roots of unity Zn. Find the order |zk|, expressed in terms of the greatest common divisor gcd(k, n). Hint. It may be easier to first express || in terms of the least common multiple lcm(k, n) of k and n and then to use the relation between gcd(k, n) and lcm(k, n).

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