List questions from cyclotomic-polynomials

Published on 26 Mar 2026 - 3:11

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Why is the restriction of being "Monic " is imposed on the divisor element?

Published on 13 Dec 2017 - 12:34

54

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Why is it the case that if $a$ is a primitive root of $x^p=1$, then $\frac{x^p-1}{x-1}=(x-a^2)(x-a^4)...(x-a^{2(p-1)})=1+x+x^2+...+x^{p-1}$?

Published on 26 Mar 2026 - 6:32

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Factorization of $X^{n}-1$ in $\mathbb{Z}[X]$

Published on 18 Dec 2017 - 17:58

252

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Non-Monic polynomials with the same discriminant as the cyclotomic polynomial.

Published on 26 Mar 2026 - 4:16

68

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Cyclotomic completion of $\mathbb{Z}[q]$

Published on 25 Dec 2017 - 12:07

236

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Determining whether $\Phi_7(x)$ is irreducible over $\mathbb{F}_{11}$

Published on 04 Jan 2018 - 21:16

65

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Find $f\in \mathbb{Z}_{p}\left[X\right]$ such that $f\left(X^{m}\right)$ is divisible by $\Phi_{p-1}$.

Published on 23 Feb 2026 - 11:40

2.2k

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Polynomials with roots of unity as roots

Published on 09 Jan 2018 - 1:13

1.3k

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Given a prime $p\in\mathbb{N}$, is $A=\frac{x^{p^{2}}-1}{x^{p}-1}$ irreducible in $\mathbb{Q}[x]$?

Published on 17 Nov 2011 - 0:51

239

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Cyclotomic polynomials in $K[X]$ are defined over the prime subfield of $K$

Published on 10 Apr 2012 - 20:21

1.6k

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Cyclotomic Polynomial of a Prime

Published on 06 Nov 2012 - 17:03

244

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Values of cyclotomic polynomial and properties of groups

Published on 21 Nov 2012 - 20:20

1.3k

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Cyclotomic Polynomials and GCD

Published on 13 Dec 2012 - 0:31

90

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Cyclotomic polynomial simplification

Published on 17 Jan 2013 - 18:15

List Question

Elements and structure of $\text{Gal}(\mathbb Q(\zeta_{21}):\mathbb Q)$

Why is the restriction of being "Monic " is imposed on the divisor element?

Why is it the case that if $a$ is a primitive root of $x^p=1$, then $\frac{x^p-1}{x-1}=(x-a^2)(x-a^4)...(x-a^{2(p-1)})=1+x+x^2+...+x^{p-1}$?

Factorization of $X^{n}-1$ in $\mathbb{Z}[X]$

Non-Monic polynomials with the same discriminant as the cyclotomic polynomial.

Cyclotomic completion of $\mathbb{Z}[q]$

Determining whether $\Phi_7(x)$ is irreducible over $\mathbb{F}_{11}$

Find $f\in \mathbb{Z}_{p}\left[X\right]$ such that $f\left(X^{m}\right)$ is divisible by $\Phi_{p-1}$.

Polynomials with roots of unity as roots

Given a prime $p\in\mathbb{N}$, is $A=\frac{x^{p^{2}}-1}{x^{p}-1}$ irreducible in $\mathbb{Q}[x]$?

Cyclotomic polynomials in $K[X]$ are defined over the prime subfield of $K$

Cyclotomic Polynomial of a Prime

Values of cyclotomic polynomial and properties of groups

Cyclotomic Polynomials and GCD

Cyclotomic polynomial simplification

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