Question

Let $L$ be the splitting field of the polynomial $ f$ over $K$, Prove that if $n!=[L:K]$, the polynomial is irreducible

score 179 · Answer 1 · 2023-09-20 06:50:55

179

Views

Let $L$ be the splitting field of the polynomial $ f$ over $K$, Prove that if $n!=[L:K]$, the polynomial is irreducible

Published on 20 Sep 2023 - 6:50

score 78 · Answer 2 · 2023-09-21 20:20:53

78

Views

Reduce Polynomial Over Real Numbers

Published on 21 Sep 2023 - 20:20

score 164 · Answer 3 · 2023-09-24 16:40:45

164

Views

Generalization of Eisenstein's Criterion

Published on 24 Sep 2023 - 16:40

score 100 · Answer 4 · 2023-09-26 12:15:51

100

Views

Find the product of all irreducible polynomials over $\mathbb{F}_p$ of degree $n$

Published on 26 Sep 2023 - 12:15

score 126 · Answer 5 · 2023-09-26 13:40:23

126

Views

Is $x^6 + bx^3 + b^2$ irreducible?

Published on 26 Sep 2023 - 13:40

score 32 · Answer 6 · 2026-03-26 14:23:03

32

Views

Primitive root of unity of irreducible factor of cyclotomic polynomial over finite field

Published on 26 Mar 2026 - 14:23

score 60 · Answer 7 · 2023-10-04 17:05:21

60

Views

Is it actually proven, that some Polynomials in the ulam spiral generate more primes than others?

Published on 04 Oct 2023 - 17:05

score 97 · Answer 8 · 2023-10-07 08:18:04

97

Views

If a monic polynomial is irreducible in $\mathbb Z_{p^k}[X]$, then it is irreducible in $\mathbb Z_p[X]$

Published on 07 Oct 2023 - 8:18

score 65 · Answer 9 · 2023-10-07 20:07:11

65

Views

Preservation of absence of univariate factors when inserting polynomials?

Published on 07 Oct 2023 - 20:07

score 145 · Answer 10 · 2023-10-07 23:44:13

145

Views

Characterization of irreducible polynomials over finite fields - alternative proof?

Published on 07 Oct 2023 - 23:44

score 191 · Answer 11 · 2023-10-11 10:53:58

191

Views

Is $x^4+15x^3+7$ irreductible on $\mathbb{Q}[x]$?

Published on 11 Oct 2023 - 10:53

score 19 · Answer 12 · 2023-10-12 20:38:32

19

Views

Which kinds of rational equations of two variables yield polynomial equations without univariate factors?

Published on 12 Oct 2023 - 20:38

score 127 · Answer 13 · 2026-03-29 03:36:45

127

Views

$x^2 + y^2 + z^2 - 2xy - 2xz - 2yz$ is irreducible over $\mathbb{Z}[x, y, z]$

Published on 29 Mar 2026 - 3:36

score 81 · Answer 14 · 2023-10-13 16:26:27

81

Views

Irreducibility of $x^n+x+1$ in $\mathbb{F}_2[x]$

Published on 13 Oct 2023 - 16:26

score 90 · Answer 15 · 2026-03-25 14:22:38

90

Views

Idempotent polynomials over the finite field $\mathbb F_p$, mod $x^p-x$.

Published on 25 Mar 2026 - 14:22

List Question

Let $L$ be the splitting field of the polynomial $ f$ over $K$, Prove that if $n!=[L:K]$, the polynomial is irreducible

Reduce Polynomial Over Real Numbers

Generalization of Eisenstein's Criterion

Find the product of all irreducible polynomials over $\mathbb{F}_p$ of degree $n$

Is $x^6 + bx^3 + b^2$ irreducible?

Primitive root of unity of irreducible factor of cyclotomic polynomial over finite field

Is it actually proven, that some Polynomials in the ulam spiral generate more primes than others?

If a monic polynomial is irreducible in $\mathbb Z_{p^k}[X]$, then it is irreducible in $\mathbb Z_p[X]$

Preservation of absence of univariate factors when inserting polynomials?

Characterization of irreducible polynomials over finite fields - alternative proof?

Is $x^4+15x^3+7$ irreductible on $\mathbb{Q}[x]$?

Which kinds of rational equations of two variables yield polynomial equations without univariate factors?

$x^2 + y^2 + z^2 - 2xy - 2xz - 2yz$ is irreducible over $\mathbb{Z}[x, y, z]$

Irreducibility of $x^n+x+1$ in $\mathbb{F}_2[x]$

Idempotent polynomials over the finite field $\mathbb F_p$, mod $x^p-x$.

Trending Questions

Popular # Hahtags

Popular Questions