List questions from irreducible-polynomials

Published on 07 Jul 2020 - 11:19

663

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Show that $x^4 + 8x - 12$ is irreducible in $\mathbb{Q}[x]$.

Published on 07 Jul 2020 - 15:19

70

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$X^3Y+Y^3+X\in \Bbb Z_2[X,Y]$ is irreducible in $\Bbb Z_2[X,Y]$

Published on 25 Mar 2026 - 7:46

42

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Can we give Gauss's Lemma (polynomial) over the integers without the primitive condition?

Published on 25 Mar 2026 - 20:19

28

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Reference request for when a polynomial has a real factorization

Published on 13 Jul 2020 - 18:27

86

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Prove that degree of a special field extension is $3$ or $6$.

Published on 15 Jul 2020 - 14:02

168

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How many subfields are there between $\mathbb{Q}$ and $\mathbb{Q}[\sqrt[16]{2}]$

Published on 16 Jul 2020 - 9:56

83

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$x^n-dy^n$ irreducible?

Published on 20 Jul 2020 - 5:32

539

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Faulhaber's polynomials and irreducibility in the sums of powers

Published on 26 Mar 2026 - 11:02

247

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A generalization of Hurwitz's theorem about prime numbers

Published on 26 Mar 2026 - 14:25

58

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Property of polynomial in $L[x]$ where $L|_k$ is an algebraic extension.

Published on 28 Jul 2020 - 8:04

209

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Irreducibility over finite fields

Published on 28 Jul 2020 - 21:41

55

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Is this polynomial irreducible over rationals?

Published on 30 Jul 2020 - 15:30

91

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Irreducibility of $f_p(x^{p^{c-1}})$ when given $f_n(x)=x^{n-1} +x^{n-2}+.....+x+1$ where $n$ is positive integer.

Published on 31 Jul 2020 - 4:26

254

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Irreducible polynomials over $\mathbb{Z}_2[x]$

Published on 06 Jul 2016 - 9:45

List Question

Irreducible polynomial equations from equations of algebraic functions in two variables?

Show that $x^4 + 8x - 12$ is irreducible in $\mathbb{Q}[x]$.

$X^3Y+Y^3+X\in \Bbb Z_2[X,Y]$ is irreducible in $\Bbb Z_2[X,Y]$

Can we give Gauss's Lemma (polynomial) over the integers without the primitive condition?

Reference request for when a polynomial has a real factorization

Prove that degree of a special field extension is $3$ or $6$.

How many subfields are there between $\mathbb{Q}$ and $\mathbb{Q}[\sqrt[16]{2}]$

$x^n-dy^n$ irreducible?

Faulhaber's polynomials and irreducibility in the sums of powers

A generalization of Hurwitz's theorem about prime numbers

Property of polynomial in $L[x]$ where $L|_k$ is an algebraic extension.

Irreducibility over finite fields

Is this polynomial irreducible over rationals?

Irreducibility of $f_p(x^{p^{c-1}})$ when given $f_n(x)=x^{n-1} +x^{n-2}+.....+x+1$ where $n$ is positive integer.

Irreducible polynomials over $\mathbb{Z}_2[x]$

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