List questions from irreducible-polynomials

Published on 03 Feb 2020 - 10:41

329

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Polynomial decomposition by Kronecker's method: usefulness of moduli

Published on 03 Feb 2020 - 11:49

495

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Order of the root of an irreducible polynomial over a finite field

Published on 04 Feb 2020 - 7:09

119

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Summation problem with prime polynomials over finite field

Published on 04 Feb 2020 - 17:11

186

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Monic polynomial irreducible modulo finitely many given primes

Published on 05 Feb 2020 - 2:17

425

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Irreducibility of $X^{4}-10X^{2}+1$ in $\mathbb{Q} [X]$...

Published on 05 Feb 2020 - 16:35

168

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Polynomials with Unit Discriminant

Published on 06 Feb 2020 - 15:26

615

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If $f, g \in \mathbb{Q}[x]$ with $fg \in \mathbb{Z}[x]$, then the product of any two coefficients is in $\mathbb{Z}$

Published on 07 Feb 2020 - 0:01

240

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Number of irreducible cubics over a field of $n$ elements.

Published on 09 Feb 2020 - 18:44

229

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Special irreducible polynomials in $k[x,y]$

Published on 11 Feb 2020 - 1:09

58

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When $d \in D$ irreducible implies $d+I \in \frac{D}{I}$ irreducible?

Published on 25 Mar 2026 - 20:15

71

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Is $x^a-y^b$ irreducible (over an arbitrary field $K$) if and only if $a$ and $b$ are coprime?

Published on 12 Feb 2020 - 5:14

2.6k

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$X^3-X-1$ irreducible in $\mathbb{Q}[X]$

Published on 12 Feb 2020 - 20:13

49

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Is $p\in k[z]$ irreducible iff $q(x,y)=y^{b\cdot\deg(p)}p(\frac{x^{a}}{y^{b}})\in k[x,y]$ is irreducible, where $a,b$ are coprime integers

Published on 13 Feb 2020 - 13:12

168

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When every prime/irreducible element remains prime/irreducible in a ring extension

Published on 25 Mar 2026 - 20:13

List Question

Prove of irreducibility of polynomial over field extension

Polynomial decomposition by Kronecker's method: usefulness of moduli

Order of the root of an irreducible polynomial over a finite field

Summation problem with prime polynomials over finite field

Monic polynomial irreducible modulo finitely many given primes

Irreducibility of $X^{4}-10X^{2}+1$ in $\mathbb{Q} [X]$...

Polynomials with Unit Discriminant

If $f, g \in \mathbb{Q}[x]$ with $fg \in \mathbb{Z}[x]$, then the product of any two coefficients is in $\mathbb{Z}$

Number of irreducible cubics over a field of $n$ elements.

Special irreducible polynomials in $k[x,y]$

When $d \in D$ irreducible implies $d+I \in \frac{D}{I}$ irreducible?

Is $x^a-y^b$ irreducible (over an arbitrary field $K$) if and only if $a$ and $b$ are coprime?

$X^3-X-1$ irreducible in $\mathbb{Q}[X]$

Is $p\in k[z]$ irreducible iff $q(x,y)=y^{b\cdot\deg(p)}p(\frac{x^{a}}{y^{b}})\in k[x,y]$ is irreducible, where $a,b$ are coprime integers

When every prime/irreducible element remains prime/irreducible in a ring extension

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