Define : primitive nth  root of unity. Show if ξ is a primitive... | Filo
Define : primitive nth  root of unity. Show if ξ is a primitive... | Filo
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Show that the number of primitive n th roots of unity is \phi(n... | Filo
Show that the number of primitive n th roots of unity is \phi(n... | Filo
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Find the number of primitive 15 th roots of unity in GF(31). | Numerade
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Let ζ7 be a primitive 7^th root of unity and let α=ζ ζ^-1. (a) Show that ζ7 is a root of the quadratic z^2-αz 1 over ℚ(α). (b) Show using the minimal polynomial for ζ7 that αis a root of the cubic x^3 x^2-2 x-1. (c) Use (a) and (b) together with the explicit solution of the cubic in (b) in the text to express ζ7 in terms of radicals similar to the expressions given earlier for the other roots of unity of small order. (The complicated nature of the expression explains why we did not include ζ7 e
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