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How quickly find we find a primitive root of unity in $\mathbb{F}_{p^z}$?

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#abstract-algebra #elementary-number-theory #algorithms #finite-fields #roots-of-unity
75
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Primitive third root of the unit

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#abstract-algebra #finite-fields #roots-of-unity #splitting-field
79
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Smallest field and root of unity

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#abstract-algebra #finite-fields #roots-of-unity #primitive-roots
74
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Calculating of sum $\sum_{z:\:z^n = 1} \frac{1}{2+z}$ with residues

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#complex-analysis #residue-calculus #roots-of-unity
52
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Determine if a $4$-th root of unity is contained in $\mathbb{F}_9$

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#abstract-algebra #solution-verification #finite-fields #roots-of-unity #primitive-roots
51
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How to express a field L in the form $M(\sqrt{d})$?

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#abstract-algebra #galois-theory #roots-of-unity #galois-extensions
69
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Finding a counter-example for Gaussian-periods for non-primes

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#field-theory #galois-theory #roots-of-unity #primitive-roots
201
Views

Splitting field of the minimal polynomial

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#abstract-algebra #finite-fields #coding-theory #minimal-polynomials #roots-of-unity
305
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Find all polynomials satisfying $p(x)p(-x)=p(x^2)$

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#polynomials #complex-numbers #roots #functional-equations #roots-of-unity
48
Views

Effect of squaring while finding roots of unity

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#complex-numbers #roots #roots-of-unity #paradoxes
28
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Roots of Unity, Curtis's rep theory text

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#abstract-algebra #field-theory #roots-of-unity
43
Views

Quadratic number fields that contain primitive root of unity

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#field-theory #extension-field #roots-of-unity #primitive-roots #cyclotomic-fields
27
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How $N(2\zeta^{2n})=2^{p-1}$?

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#abstract-algebra #field-theory #normed-spaces #roots-of-unity
216
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If $a_i\in\mathbb{R}$, $\omega^2+\omega+1=0$, and $\sum_{i=1}^n\frac{1}{a_i+\omega^k} =2\omega^{2k}$ for $k=1,2$, find $\sum_{i=1}^n\frac{1}{a_i+1}$.

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#complex-numbers #summation #rational-functions #roots-of-unity #meromorphic-functions
418
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Which integer combinations of $n$-th roots of unity are zero?

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#elementary-number-theory #polynomials #complex-numbers #roots-of-unity #cyclotomic-polynomials

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