List questions from irreducible-polynomials

Published on 05 Apr 2026 - 20:02

106

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Showing that a polynomial in $k[x_1, \dots, x_n]$ is irreducible

Published on 13 Dec 2020 - 10:42

167

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Truncated expresion of $e^x$ is an irreducible polynomial

Published on 13 Dec 2020 - 17:59

32

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Does every field extension of a field containing irreducible polynomial have a root?

Published on 17 Dec 2020 - 20:53

145

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Why is $x^4+x^3+x^2+x+1$ irreducible over $\mathbb{Q}_3$?

Published on 04 Apr 2026 - 8:11

171

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Polynomial $f(X) g(Y)- g(X) f(Y)$ irreducible in $F[X,Y]$?

Published on 21 Dec 2020 - 23:01

144

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Polynomial $f(X) g(Y)- g(X) f(Y)$ cannot be divided by a non-constant $h(X) \in F[X]$

Published on 22 Dec 2020 - 22:21

60

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general Complex solution of irreducible quartic polynomial

Published on 09 Apr 2026 - 20:52

1.1k

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If $a_1, a_2, \ldots, a_n$ are distinct integers, then prove that $(x-a_1)(x-a_2)\cdots(x-a_n)-1$ is irreducible over integers.

Published on 26 Dec 2020 - 11:20

198

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$\operatorname{dim} \mathbb{Q}[2^{1/n},3^{1/m}] / \mathbb{Q} = nm$

Published on 26 Dec 2020 - 16:42

108

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Irreducibility of certain polynomials

Published on 26 Dec 2020 - 23:42

80

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Irreducible polynomials over $\mathbb{Q}$?

Published on 27 Dec 2020 - 15:16

296

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Degree of $\mathbb{Q}(2^{\frac{1}{3}},\omega)$ over $\mathbb{Q}(2^{\frac{1}{3}})$

Published on 02 Apr 2026 - 17:31

48

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Number of factors of irreducible polynomial of degree $mn$ over $\mathbb{F}_p$ in $\mathbb{F}_{p^n}[x].$

Published on 29 Dec 2020 - 22:01

81

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Maintaining Polynomial Irreducibility

Published on 11 Apr 2026 - 10:05

List Question

How to factor $x^5-1$ for binary codes

Showing that a polynomial in $k[x_1, \dots, x_n]$ is irreducible

Truncated expresion of $e^x$ is an irreducible polynomial

Does every field extension of a field containing irreducible polynomial have a root?

Why is $x^4+x^3+x^2+x+1$ irreducible over $\mathbb{Q}_3$?

Polynomial $f(X) g(Y)- g(X) f(Y)$ irreducible in $F[X,Y]$?

Polynomial $f(X) g(Y)- g(X) f(Y)$ cannot be divided by a non-constant $h(X) \in F[X]$

general Complex solution of irreducible quartic polynomial

If $a_1, a_2, \ldots, a_n$ are distinct integers, then prove that $(x-a_1)(x-a_2)\cdots(x-a_n)-1$ is irreducible over integers.

$\operatorname{dim} \mathbb{Q}[2^{1/n},3^{1/m}] / \mathbb{Q} = nm$

Irreducibility of certain polynomials

Irreducible polynomials over $\mathbb{Q}$?

Degree of $\mathbb{Q}(2^{\frac{1}{3}},\omega)$ over $\mathbb{Q}(2^{\frac{1}{3}})$

Number of factors of irreducible polynomial of degree $mn$ over $\mathbb{F}_p$ in $\mathbb{F}_{p^n}[x].$

Maintaining Polynomial Irreducibility

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