An nth root of unity ε is an element such that en-1. We say that εis primitive if every nth root of unity is ek for some k. Show that thereis przmatwe if every nth root of unity 1s *forksomeare primitive nth roots of unity En E C for all n, and find the degree ofQQ(En) for 1 < n

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Asked Apr 25, 2019
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Abstract Algebra. Answer in detail please.

An nth root of unity ε is an element such that en-1. We say that ε
is primitive if every nth root of unity is ek for some k. Show that there
is przmatwe if every nth root of unity 1s *
for
k
some
are primitive nth roots of unity En E C for all n, and find the degree of
QQ(En) for 1 < n <6
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An nth root of unity ε is an element such that en-1. We say that ε is primitive if every nth root of unity is ek for some k. Show that there is przmatwe if every nth root of unity 1s * for k some are primitive nth roots of unity En E C for all n, and find the degree of QQ(En) for 1 < n <6

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Expert Answer

Step 1

An nth root of unity ε is an element such that εn = 1. It is said that ε is primitive if every nth root of unity is εk for some k. To show: There are primitive nth roots of unity

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Step 2

As it is given ε is primitive and εk is the nth root of unity, by definition of nth root of unity we can say

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Step 3

Denote the nth root of unity ε = &epsi...

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