The field contains a th primitive root of unity if and only if is a divisor of ; if is a divisor of , then the number of primitive th roots of unity in is (Euler's totient function). The number of th roots of unity in is .
The field contains a th primitive root of unity if and only if is a divisor of ; if is a divisor of  then the number of primitive th roots of unity in is (Euler's totient function) The number of th roots of unity in is 