We say a complex number z is a primitive nth root of unity if but for 0<m<n. Show that is a primitive nth root of unity if and only if gcd(k,n)=1.
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Originally Posted by meggnog We say a complex number z is a primitive nth root of unity if but for 0<m<n. Show that is a primitive nth root of unity if and only if gcd(k,n)=1. Assume and suppose . . Thus is not primitive. If and , then where . Thus . So we see is primitive.
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