List questions from cyclotomic-polynomials

Published on 14 Apr 2026 - 18:29

516

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Polynomial with positive coefficients

Published on 09 Apr 2026 - 0:08

68

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

Published on 17 Apr 2026 - 0:42

150

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

Published on 26 Mar 2026 - 8:04

35

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

Published on 14 Apr 2026 - 5:48

131

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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 11 May 2026 - 2:06

84

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

Published on 13 Apr 2026 - 13:30

102

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

Published on 16 Apr 2026 - 8:14

717

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prove cyclotomic polynomial is a minimal polynomial

Published on 14 Apr 2026 - 4:36

73

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

Published on 26 Mar 2026 - 6:26

86

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

Published on 17 Apr 2026 - 6:43

114

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

Published on 12 Apr 2026 - 1:24

51

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

Published on 10 May 2026 - 21:24

99

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how solve Cyclotomic Polynomial , n=8

Published on 13 Apr 2026 - 10:06

210

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how can find cyclotomic Polynomial where n=105

Published on 11 Apr 2026 - 13:45

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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