List questions from cyclotomic-polynomials

Published on 20 Apr 2020 - 11:25

73

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How can I show that $1+x+...+x^{n-1}$ divides any polynomial with distinct exponents mod n?

Published on 13 May 2020 - 1:43

121

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Cyclotomic polynomial for any positive integer

Published on 25 Mar 2026 - 9:46

74

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Irreducibilty Cyclotomic polynomial $f(x^{n})$

Published on 23 May 2020 - 16:41

125

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Unit roots group is isomorphic to $\Bbb{Q}/\Bbb{Z}\left[\frac{1}{p}\right]$ in a field of characteristic $p\ge0$

Published on 25 Mar 2026 - 11:24

170

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Factoring $x^{2020} + x^{2019} + \cdots + x + 1$ on $\mathbb Q[x]$

Published on 29 May 2020 - 4:20

130

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Find all fields $\mathbb{Q} \subset E \subset \mathbb{Q}(\zeta_{40})$ with $[E:\mathbb{Q}]=2$

Published on 10 Jun 2020 - 12:53

209

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$f(1)+f(-1)=0$ prove $f(x)$ does not divide $x^n -1$

Published on 17 Jun 2020 - 2:44

153

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Proof? of irreducibility of cyclotomic polynomial

Published on 29 Jun 2020 - 22:10

323

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Does $\Phi_n(\alpha)=0$ in $\Bbb{F}_p$ for some $\alpha\in\mathbb{F}_p$ imply that $\mathrm{ord}_p(\alpha) = n$?

Published on 30 Jun 2020 - 9:11

135

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Generators of a Power of a Prime Ideal

Published on 25 Mar 2026 - 11:32

31

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Properties of a certain divisor of the $m^{\rm th}$ root of unity in the $m^{\rm th}$ cyclotomic ring.

Published on 25 Mar 2026 - 11:27

417

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Which integer combinations of $n$-th roots of unity are zero?

Published on 22 Jul 2020 - 6:10

237

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Primality testing using cyclotomic polynomials

Published on 26 Jul 2020 - 11:35

59

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$p$ is an odd prime less than $m$ and $a\in \mathbb Z$ then $p|a^m-1$ implies $p|m$

Published on 27 Jul 2020 - 7:34

List Question

Cyclotomic Polynomials: Example

How can I show that $1+x+...+x^{n-1}$ divides any polynomial with distinct exponents mod n?

Cyclotomic polynomial for any positive integer

Irreducibilty Cyclotomic polynomial $f(x^{n})$

Unit roots group is isomorphic to $\Bbb{Q}/\Bbb{Z}\left[\frac{1}{p}\right]$ in a field of characteristic $p\ge0$

Factoring $x^{2020} + x^{2019} + \cdots + x + 1$ on $\mathbb Q[x]$

Find all fields $\mathbb{Q} \subset E \subset \mathbb{Q}(\zeta_{40})$ with $[E:\mathbb{Q}]=2$

$f(1)+f(-1)=0$ prove $f(x)$ does not divide $x^n -1$

Proof? of irreducibility of cyclotomic polynomial

Does $\Phi_n(\alpha)=0$ in $\Bbb{F}_p$ for some $\alpha\in\mathbb{F}_p$ imply that $\mathrm{ord}_p(\alpha) = n$?

Generators of a Power of a Prime Ideal

Properties of a certain divisor of the $m^{\rm th}$ root of unity in the $m^{\rm th}$ cyclotomic ring.

Which integer combinations of $n$-th roots of unity are zero?

Primality testing using cyclotomic polynomials

$p$ is an odd prime less than $m$ and $a\in \mathbb Z$ then $p|a^m-1$ implies $p|m$

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