List questions from cyclotomic-polynomials

Published on 15 Jan 2021 - 12:02

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Prove that the splitting field of $x^p-1$ for p an odd prime contains a unique intermediate field of degree 2

Published on 16 Jan 2021 - 7:28

79

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A question related to cyclotomic polynomials in -x

Published on 24 Jan 2021 - 12:35

157

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Can $\Phi_n(\Phi_n(n))$ be a prime number?

Published on 31 Jan 2021 - 9:13

41

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How many Carmichael numbers exist of the form $\Phi_n(b)$ for $n>6$?

Published on 23 Feb 2026 - 6:59

44

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Can we rule out $\ p\mid t\ $ , if $\ p\mid \phi_t(n)\ $?

Published on 23 Feb 2021 - 13:29

84

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Tight bounds for $\Phi_n(b)$?

Published on 01 Mar 2021 - 13:36

55

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Smallest prime of the form $\phi_{21209}(n)$?

Published on 24 Mar 2021 - 12:28

53

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Prime number of the form $\phi_n(n^p)$?

Published on 24 Mar 2021 - 12:39

79

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$p_1^x\equiv p_2^x\equiv 1 \pmod{p_1p_2-1}$ problem

Published on 30 Apr 2021 - 14:27

183

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Book recommendation/reference request on a gentle introduction to cyclotomic polynomials

Published on 27 Mar 2026 - 14:39

55

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How to prove that $\Pi_{1 \leq j \leq p^n, p \nmid j}((\zeta_{p^n}^j)^{p^{n-1}}-1) = p^{p^{n-1}}$?

Published on 26 Mar 2026 - 8:02

55

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For $\omega=e^{2\pi i/q}$ and $c_0,\ldots,c_{q-1}\in \mathbb Z$, $\sum\limits_{k=0}^{q-1}c_k\omega^k \equiv \sum\limits_{k=0}^{q-1}c_k\pmod p$.

Published on 09 Jul 2021 - 5:52

154

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Smallest $p$ such that $2\mid\operatorname{ord}(a)$ in $\mathbb{Z}/p\mathbb{Z}$

Published on 26 Jul 2021 - 2:05

216

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Prove $Q_{mp} = Q_{m}(x^p)$ when prime $p$ divides $m$. ($Q$ is cyclotomic polynomial over some finite field $K$)

Published on 08 Aug 2021 - 11:02

List Question

Is the "cyclotomic diagonalization" always squarefree?

Prove that the splitting field of $x^p-1$ for p an odd prime contains a unique intermediate field of degree 2

A question related to cyclotomic polynomials in -x

Can $\Phi_n(\Phi_n(n))$ be a prime number?

How many Carmichael numbers exist of the form $\Phi_n(b)$ for $n>6$?

Can we rule out $\ p\mid t\ $ , if $\ p\mid \phi_t(n)\ $?

Tight bounds for $\Phi_n(b)$?

Smallest prime of the form $\phi_{21209}(n)$?

Prime number of the form $\phi_n(n^p)$?

$p_1^x\equiv p_2^x\equiv 1 \pmod{p_1p_2-1}$ problem

Book recommendation/reference request on a gentle introduction to cyclotomic polynomials

How to prove that $\Pi_{1 \leq j \leq p^n, p \nmid j}((\zeta_{p^n}^j)^{p^{n-1}}-1) = p^{p^{n-1}}$?

For $\omega=e^{2\pi i/q}$ and $c_0,\ldots,c_{q-1}\in \mathbb Z$, $\sum\limits_{k=0}^{q-1}c_k\omega^k \equiv \sum\limits_{k=0}^{q-1}c_k\pmod p$.

Smallest $p$ such that $2\mid\operatorname{ord}(a)$ in $\mathbb{Z}/p\mathbb{Z}$

Prove $Q_{mp} = Q_{m}(x^p)$ when prime $p$ divides $m$. ($Q$ is cyclotomic polynomial over some finite field $K$)

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