List questions from cyclotomic-polynomials

Published on 18 Dec 2014 - 2:16

513

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Polynomial with positive coefficients

Published on 24 Dec 2014 - 18:16

65

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Show that $\Phi_{p^n}(X)=\Phi_p(X^{p^{n-1}})$ with $p$ prime.

Published on 01 Jan 2015 - 15:24

149

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Is this an n-th root of unity (on the regular polygon)?

Published on 07 Oct 2019 - 15:09

33

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Show that every integer is the coefficient of some $\Phi_n(x)$

Published on 10 Oct 2019 - 19:40

130

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Quotients in cyclotomic fields: $\mathbb{Z} [\zeta_{pqr}] /(1 - \zeta_p,1 - \zeta_q) \cong \mathbb{Z} [\zeta_{r}] /(pq) $?

Published on 25 Mar 2026 - 6:30

81

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Question about the proof of the irreducibility of cyclotomic polynomials in Dummit & Foote

Published on 26 Oct 2019 - 7:11

99

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How to prove that if $p\mid n$, then $\Phi_{pn}(x)=\Phi_n(x^p)$?

Published on 30 Oct 2019 - 1:10

714

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prove cyclotomic polynomial is a minimal polynomial

Published on 03 Nov 2019 - 10:34

72

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How does the galois group behaves with polynomial w/ an example??

Published on 14 Nov 2019 - 5:25

81

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What will be $\text {Ord}_n\ q$?

Published on 15 Nov 2019 - 16:26

111

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How many prime factors will $\Phi_n$ have in its prime factorization?

Published on 16 Nov 2019 - 16:08

50

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$\Phi_{2^n}(x) = x^{2^{n-1}}+1$ by Mobius Inversion

Published on 25 Mar 2026 - 11:25

96

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how solve Cyclotomic Polynomial , n=8

Published on 30 Dec 2019 - 14:44

207

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how can find cyclotomic Polynomial where n=105

Published on 30 Dec 2019 - 16:13

List Question

How many non-rational complex numbers $x$ have the property that $x^n$ and $(x+1)^n$ are rational?

Polynomial with positive coefficients

Show that $\Phi_{p^n}(X)=\Phi_p(X^{p^{n-1}})$ with $p$ prime.

Is this an n-th root of unity (on the regular polygon)?

Show that every integer is the coefficient of some $\Phi_n(x)$

Quotients in cyclotomic fields: $\mathbb{Z} [\zeta_{pqr}] /(1 - \zeta_p,1 - \zeta_q) \cong \mathbb{Z} [\zeta_{r}] /(pq) $?

Question about the proof of the irreducibility of cyclotomic polynomials in Dummit & Foote

How to prove that if $p\mid n$, then $\Phi_{pn}(x)=\Phi_n(x^p)$?

prove cyclotomic polynomial is a minimal polynomial

How does the galois group behaves with polynomial w/ an example??

What will be $\text {Ord}_n\ q$?

How many prime factors will $\Phi_n$ have in its prime factorization?

$\Phi_{2^n}(x) = x^{2^{n-1}}+1$ by Mobius Inversion

how solve Cyclotomic Polynomial , n=8

how can find cyclotomic Polynomial where n=105

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