Let and let be an -th primitive root of unity. Prove that

where denotes the Euler’s totient function.

**Solution**

We have

where since is the minimal polynomial of over .

The result follows.

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Let and let be an -th primitive root of unity. Prove that

where denotes the Euler’s totient function.

**Solution**

We have

where since is the minimal polynomial of over .

The result follows.