List questions from irreducible-polynomials

Published on 19 Jun 2019 - 11:47

135

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Monic polynomials $f\in R[x]$ with $f-a$ irreducible for almost all values of $a\in R$

Published on 23 Jun 2019 - 22:06

641

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Show that $x^4 + x^3 + 1, x^4 + x^3 + x^2 + x + 1$ are irreducible over $GF(4), GF(8)$

Published on 25 Jun 2019 - 10:37

221

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For $\alpha = \sqrt[3]{2} + i$, find the minimal polynomial over $\mathbb{Q}$ and over $\mathbb{Q}[\sqrt[3]{2}]$

Published on 27 Jun 2019 - 15:30

790

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$x^a+ y^b + z^c$ is irreducible in $\mathbb C[x,y,z]$

Published on 25 Mar 2026 - 4:41

105

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Factorization in $\mathbb{Z}[x]$?

Published on 25 Mar 2026 - 12:13

59

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Is it true that $\forall f \in \mathbb{Z}[x],\exists p$ prime number, s.t. $ f $ is reducible in $\mathbb{F}_p$?

Published on 02 Jul 2019 - 3:04

321

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Number of irreducible monic polynomials of degree $3$ over $\Bbb F_p$, $p$ prime

Published on 25 Mar 2026 - 13:57

48

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question about polynomial residue field to solve code theory problem

Published on 26 Mar 2026 - 19:38

167

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Rational polynomial of degree n with n-2 real roots, 2 complex roots and Galois group not being $S_n$

Published on 07 Jul 2019 - 23:05

171

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Irreducibility of a polynomial in a finite field

Published on 09 Jul 2019 - 18:22

91

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A condition for a primitive polynomial to be irreducible.

Published on 11 Jul 2019 - 14:01

118

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Show that the ideal $I = 3\mathbb Z[x] + (x^3-x^2+2x-1)\mathbb Z[x]$ is not a principal ideal of $\mathbb Z[x]$

Published on 12 Jul 2019 - 16:03

618

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Prove that $(x^2+x)^{2^n}+1$ is irreducible

Published on 12 Jul 2019 - 19:04

1.3k

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Irreducibility of prime degree cyclotomic polynomials

Published on 25 Mar 2026 - 22:10

List Question

Irreducible polynomial over $\Bbb Q$

Monic polynomials $f\in R[x]$ with $f-a$ irreducible for almost all values of $a\in R$

Show that $x^4 + x^3 + 1, x^4 + x^3 + x^2 + x + 1$ are irreducible over $GF(4), GF(8)$

For $\alpha = \sqrt[3]{2} + i$, find the minimal polynomial over $\mathbb{Q}$ and over $\mathbb{Q}[\sqrt[3]{2}]$

$x^a+ y^b + z^c$ is irreducible in $\mathbb C[x,y,z]$

Factorization in $\mathbb{Z}[x]$?

Is it true that $\forall f \in \mathbb{Z}[x],\exists p$ prime number, s.t. $ f $ is reducible in $\mathbb{F}_p$?

Number of irreducible monic polynomials of degree $3$ over $\Bbb F_p$, $p$ prime

question about polynomial residue field to solve code theory problem

Rational polynomial of degree n with n-2 real roots, 2 complex roots and Galois group not being $S_n$

Irreducibility of a polynomial in a finite field

A condition for a primitive polynomial to be irreducible.

Show that the ideal $I = 3\mathbb Z[x] + (x^3-x^2+2x-1)\mathbb Z[x]$ is not a principal ideal of $\mathbb Z[x]$

Prove that $(x^2+x)^{2^n}+1$ is irreducible

Irreducibility of prime degree cyclotomic polynomials

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