**Definition.** *Let E be a field, and let n be a positive integer. An element * *is called a primitive nth root of unity in E if ω*^{n} = 1, *but ω*^{m} ≠ 1 *for any positive integer m *<* n*.

Note that the complex numbers satisfying *x*^{n} = 1 form a finite subgroup *H *of the multiplicative group of the nonzero elements of the field **C** of complex numbers. Also *H *is a cyclic group generated by any primitive *n*th root *ω *of unity. There are exactly primitive *n*th roots ...

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