List questions from cyclotomic-polynomials

Published on 26 Mar 2026 - 12:07

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$K/\Bbb Q< \infty$ extension and a prime $p\nmid |K:\Bbb Q|$ with $\zeta_p \notin K$. Is $\Phi_p(X)$ is irreducible over $K$?

Published on 09 Aug 2021 - 15:33

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For fixed positive integers $a,k$ prove that there are infinitely many primes $p$ for which $p\equiv 1\pmod{k}$ and $a$ is a $k$'th power mod $p$

Published on 30 Sep 2021 - 8:47

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Norm of generator of prime ideal

Published on 26 Mar 2026 - 12:37

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Why is $\mathbb{Q}[\zeta_{p}] = \{a_{0}, a_{1}\zeta, \dots, a_{p-2}\zeta^{p-2}, a_{i} \in \mathbb{Q}\}$, where $p \geq 2$ is a prime?

Published on 26 Mar 2026 - 11:01

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Cyclotomic polynomial with nonnegative coefficients

Published on 09 Oct 2021 - 19:25

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Is $g(x,y)= \frac{f(x^{2y+1},y)}{f(x,y)}$ always an integer?

Published on 10 Oct 2021 - 15:08

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factoring a cyclotomic polynomial modulo a prime

Published on 10 Oct 2021 - 18:38

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How to prove $X^{4}+X^{3}+X^{2}+X+1$ is irreductible in $\mathbb{F}_{2}$

Published on 27 Mar 2026 - 17:04

103

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What can be said about the primality of Zsigmondy Numbers?

Published on 23 Feb 2026 - 12:07

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Order and Structure of Galois group

Published on 24 Nov 2021 - 21:26

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Particular case of the law of quadratic reciprocity

Published on 26 Mar 2026 - 14:34

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Simple proof that n divides $\sum_{1\le k<n, \gcd(k,n)=1} k$

Published on 03 Jan 2022 - 17:21

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Calculate $N(1-\xi_m)$, where $\xi_m= e^{\frac{2\pi i}{m}}$ and $m=p^l$

Published on 04 Jan 2022 - 16:12

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How to write an arbitrary element of cyclotomic extension of 6th root of unity?

Published on 26 Mar 2026 - 12:37

List Question

What is the discriminant of $\Phi_{2}(X)$ over $\Bbb Q$?

$K/\Bbb Q< \infty$ extension and a prime $p\nmid |K:\Bbb Q|$ with $\zeta_p \notin K$. Is $\Phi_p(X)$ is irreducible over $K$?

For fixed positive integers $a,k$ prove that there are infinitely many primes $p$ for which $p\equiv 1\pmod{k}$ and $a$ is a $k$'th power mod $p$

Norm of generator of prime ideal

Why is $\mathbb{Q}[\zeta_{p}] = \{a_{0}, a_{1}\zeta, \dots, a_{p-2}\zeta^{p-2}, a_{i} \in \mathbb{Q}\}$, where $p \geq 2$ is a prime?

Cyclotomic polynomial with nonnegative coefficients

Is $g(x,y)= \frac{f(x^{2y+1},y)}{f(x,y)}$ always an integer?

factoring a cyclotomic polynomial modulo a prime

How to prove $X^{4}+X^{3}+X^{2}+X+1$ is irreductible in $\mathbb{F}_{2}$

What can be said about the primality of Zsigmondy Numbers?

Order and Structure of Galois group

Particular case of the law of quadratic reciprocity

Simple proof that n divides $\sum_{1\le k<n, \gcd(k,n)=1} k$

Calculate $N(1-\xi_m)$, where $\xi_m= e^{\frac{2\pi i}{m}}$ and $m=p^l$

How to write an arbitrary element of cyclotomic extension of 6th root of unity?

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