Question

What is the Galois Group of $X^5 + 5 X^3+5 X^2+4 X+1 \in \mathbb{Q}[X]$?

score 128 · Answer 1 · 2018-05-30 11:54:05

128

Views

What is the Galois Group of $X^5 + 5 X^3+5 X^2+4 X+1 \in \mathbb{Q}[X]$?

Published on 30 May 2018 - 11:54

score 45 · Answer 2 · 2018-05-30 19:11:23

45

Views

Am I interpreting this theorem correctly?

Published on 30 May 2018 - 19:11

score 197 · Answer 3 · 2018-05-30 19:23:47

197

Views

Is there an irreducible, degree 7 polynomial in $\mathbb{Q}[x]$ which has exactly two of its roots in $\mathbb{C-R}$?

Published on 30 May 2018 - 19:23

score 173 · Answer 4 · 2018-05-30 20:27:32

173

Views

Proving that $x^7-120x^5+1875x^3+12500x+5$ has exactly 5 real roots

Published on 30 May 2018 - 20:27

score 545 · Answer 5 · 2026-03-25 05:41:32

545

Views

What are the intermediate fields of $\mathbb{Q}(\sqrt[4]{2},i)/\mathbb{Q}$ of order $4$ over $\mathbb{Q}$?

Published on 25 Mar 2026 - 5:41

score 94 · Answer 6 · 2018-06-04 13:32:32

94

Views

Weak Nullstellensatz in practice

Published on 04 Jun 2018 - 13:32

score 769 · Answer 7 · 2018-06-04 21:51:54

769

Views

What is the Galois group of $f = X^4 - 3X^2+3 \in \mathbb{Q}[X]$?

Published on 04 Jun 2018 - 21:51

score 105 · Answer 8 · 2018-06-06 09:27:26

105

Views

Where is the flaw in my reasoning about the number of irreducible degree 9 polynomials over $\mathbb F_2$?

Published on 06 Jun 2018 - 9:27

score 52 · Answer 9 · 2018-06-06 13:43:16

52

Views

Showing a polynomial is irreducible.

Published on 06 Jun 2018 - 13:43

score 172 · Answer 10 · 2018-06-07 18:01:51

172

Views

Irreducibility of a polynomial linked to his reduction mod $m$

Published on 07 Jun 2018 - 18:01

score 60 · Answer 11 · 2018-06-07 18:52:21

60

Views

Example of a polynomial in $\mathbb{F}_q[x]$ for which the density of square-free values approaches some limit.

Published on 07 Jun 2018 - 18:52

score 933 · Answer 12 · 2018-06-09 09:03:23

933

Views

Polynomial decomposition into irreducible factors

Published on 09 Jun 2018 - 9:03

score 182 · Answer 13 · 2026-03-22 22:04:56

182

Views

A field with an irreducible, separable polynomial with roots $\alpha$ and $\alpha + 1$ must have positive characteristic.

Published on 22 Mar 2026 - 22:04

score 300 · Answer 14 · 2018-06-10 15:51:58

300

Views

Prime Polynomial and roots

Published on 10 Jun 2018 - 15:51

score 580 · Answer 15 · 2018-06-10 17:21:52

580

Views

Does every polynomial over a finite field have a square root modulo an irreducible polynomial?

Published on 10 Jun 2018 - 17:21

List Question

What is the Galois Group of $X^5 + 5 X^3+5 X^2+4 X+1 \in \mathbb{Q}[X]$?

Am I interpreting this theorem correctly?

Is there an irreducible, degree 7 polynomial in $\mathbb{Q}[x]$ which has exactly two of its roots in $\mathbb{C-R}$?

Proving that $x^7-120x^5+1875x^3+12500x+5$ has exactly 5 real roots

What are the intermediate fields of $\mathbb{Q}(\sqrt[4]{2},i)/\mathbb{Q}$ of order $4$ over $\mathbb{Q}$?

Weak Nullstellensatz in practice

What is the Galois group of $f = X^4 - 3X^2+3 \in \mathbb{Q}[X]$?

Where is the flaw in my reasoning about the number of irreducible degree 9 polynomials over $\mathbb F_2$?

Showing a polynomial is irreducible.

Irreducibility of a polynomial linked to his reduction mod $m$

Example of a polynomial in $\mathbb{F}_q[x]$ for which the density of square-free values approaches some limit.

Polynomial decomposition into irreducible factors

A field with an irreducible, separable polynomial with roots $\alpha$ and $\alpha + 1$ must have positive characteristic.

Prime Polynomial and roots

Does every polynomial over a finite field have a square root modulo an irreducible polynomial?

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