List questions from cyclotomic-polynomials

Published on 12 Apr 2026 - 14:54

76

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

Published on 14 Apr 2026 - 16:36

122

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Cyclotomic polynomial for any positive integer

Published on 11 May 2026 - 8:21

77

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

Published on 15 Apr 2026 - 18:07

126

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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 11 May 2026 - 5:46

172

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

Published on 17 Apr 2026 - 6:23

133

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

Published on 17 Apr 2026 - 12:23

212

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

Published on 17 Apr 2026 - 13:50

156

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Proof? of irreducibility of cyclotomic polynomial

Published on 14 Apr 2026 - 6:28

326

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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 16 Apr 2026 - 19:57

136

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Generators of a Power of a Prime Ideal

Published on 11 May 2026 - 5:25

32

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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 11 May 2026 - 6:47

422

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

Published on 17 Apr 2026 - 10:44

241

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Primality testing using cyclotomic polynomials

Published on 11 May 2026 - 2:01

62

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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 17 Apr 2026 - 2:37

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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