List questions from cyclotomic-polynomials

Published on 11 Mar 2022 - 6:08

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If $s = 4m - 3$, then $\sigma(p^s) = (1 + p^{2m-1})(1 + p + \ldots + p^{2m-2})$. Is there a similar factorization for $\sigma(q^t)$ when $t=4n$?

Published on 11 Mar 2022 - 7:12

64

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Question on cyclotomic polynomials and the Möbius function

Published on 27 Mar 2026 - 18:17

330

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Show that $1+\zeta+\dots+\zeta^{k-1}$ is a unit

Published on 26 Mar 2026 - 16:09

128

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Factoring cyclotomic polynomials in tree form

Published on 26 Mar 2026 - 14:19

74

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On some congruence in cyclotomic field

Published on 26 Mar 2026 - 14:24

177

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Cyclotomic Polynomial Proof

Published on 26 Mar 2026 - 14:17

219

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Find $a \in \mathbb C$ such that $\mathbb Q (\zeta_5)= \mathbb Q(\sqrt 5, a)$ and $\left[ \mathbb Q(a): \mathbb Q \right]=2 $.

Published on 26 Mar 2026 - 14:20

60

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What is the correspondent sub-field of this cyclotomic extension, given by the Fundamental Theorem of Galois Theory?

Published on 17 Aug 2022 - 0:59

45

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Constructing intersections in a regular polygon

Published on 22 Aug 2022 - 12:19

110

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$x^4+x^3+x^2+x+1$ is irreducible over $\mathbb{F}_2$

Published on 31 Aug 2022 - 15:04

184

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"Easy" proof that $\Phi_n$ has degree $\phi_n$

Published on 26 Mar 2026 - 14:19

151

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If $P(P(x))=x^{36}$, does it imply $P(x)=x^6$?

Published on 26 Mar 2026 - 16:06

62

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How to prove that: Automorphism $\zeta_n\to\zeta_n^p$ leaves prime ideal factor of p unchanged.

Published on 26 Mar 2026 - 16:10

86

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Solutions of $(x^p - y^p)/(x - y) = z^p $

Published on 04 Oct 2022 - 21:04

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Some questions on cyclotomic polynomials

If $s = 4m - 3$, then $\sigma(p^s) = (1 + p^{2m-1})(1 + p + \ldots + p^{2m-2})$. Is there a similar factorization for $\sigma(q^t)$ when $t=4n$?

Question on cyclotomic polynomials and the Möbius function

Show that $1+\zeta+\dots+\zeta^{k-1}$ is a unit

Factoring cyclotomic polynomials in tree form

On some congruence in cyclotomic field

Cyclotomic Polynomial Proof

Find $a \in \mathbb C$ such that $\mathbb Q (\zeta_5)= \mathbb Q(\sqrt 5, a)$ and $\left[ \mathbb Q(a): \mathbb Q \right]=2 $.

What is the correspondent sub-field of this cyclotomic extension, given by the Fundamental Theorem of Galois Theory?

Constructing intersections in a regular polygon

$x^4+x^3+x^2+x+1$ is irreducible over $\mathbb{F}_2$

"Easy" proof that $\Phi_n$ has degree $\phi_n$

If $P(P(x))=x^{36}$, does it imply $P(x)=x^6$?

How to prove that: Automorphism $\zeta_n\to\zeta_n^p$ leaves prime ideal factor of p unchanged.

Solutions of $(x^p - y^p)/(x - y) = z^p $

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