Question

Galois groups of $x^3-3x+1$ and $(x^3-2)(x^2+3)$ over $\mathbb{Q}$

score 5.1k · Answer 1 · 2026-03-28 21:06:57

5.1k

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Galois groups of $x^3-3x+1$ and $(x^3-2)(x^2+3)$ over $\mathbb{Q}$

Published on 28 Mar 2026 - 21:06

score 223 · Answer 2 · 2016-06-02 23:22:28

223

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Using the discriminant to find Galois group of a quartic

Published on 02 Jun 2016 - 23:22

score 708 · Answer 3 · 2016-06-03 10:32:19

708

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How To Prove That The Rijndael Polynomial Is Irreducible?

Published on 03 Jun 2016 - 10:32

score 296 · Answer 4 · 2026-03-29 18:11:58

296

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what does $\alpha$ signify in finite fields modular arithmetic

Published on 29 Mar 2026 - 18:11

score 159 · Answer 5 · 2026-03-27 04:17:31

159

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Proof that $a^{n}+b^{n}$ is irreducible over $\mathbb Q$

Published on 27 Mar 2026 - 4:17

score 26 · Answer 6 · 2026-03-22 21:21:41

26

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Let $P$ $\in$ $\mathbb{F}_{p}[x,y]$, if $P$ does not have multiple factors then $P-1$ is irreducible.

Published on 22 Mar 2026 - 21:21

score 8k · Answer 7 · 2026-03-27 04:21:49

8k

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Prove that $X^4+X^3+X^2+X+1$ is irreducible in $\mathbb{Q}[X]$, but that it has two different irreducible factors in $\mathbb{R}[X]$

Published on 27 Mar 2026 - 4:21

score 165 · Answer 8 · 2026-03-25 14:07:00

165

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Leading term ideal irreducible iff the ideal is irreducible?

Published on 25 Mar 2026 - 14:07

score 198 · Answer 9 · 2016-06-07 22:44:13

198

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Seeking an "easy " way to show that $p(x)=x^6+\cdots+x^2+x+1$ is irreducible over $\Bbb{Z_{17}}$

Published on 07 Jun 2016 - 22:44

score 188 · Answer 10 · 2016-06-08 16:30:12

188

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Knowing the Galois group of the splitting field of a polynomial $f$, how can I show that $f$ is irreducible in the ground field?

Published on 08 Jun 2016 - 16:30

score 61 · Answer 11 · 2016-06-09 17:01:26

61

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Show that $f(x)=x^3+(2+i)x+(1+i)$ is irreducible in $\mathbb{Z}[i][x]$

Published on 09 Jun 2016 - 17:01

score 65 · Answer 12 · 2016-06-13 19:58:33

65

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Give two polynomials in $\mathbb Q[x]$ (of degree 2 and 3) such that their product is an irreducible polynomial in $\mathbb Q[x]$ of degree 5

Published on 13 Jun 2016 - 19:58

score 56 · Answer 13 · 2016-06-13 20:26:51

56

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Is it possible to have a such polynomials?

Published on 13 Jun 2016 - 20:26

score 129 · Answer 14 · 2016-06-13 22:12:54

129

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Why are these two calculations in $GF(2^5)$ not equal

Published on 13 Jun 2016 - 22:12

score 75 · Answer 15 · 2016-06-14 15:00:54

75

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Question on splitting field and irreducible polynomials.

Published on 14 Jun 2016 - 15:00

List Question

Galois groups of $x^3-3x+1$ and $(x^3-2)(x^2+3)$ over $\mathbb{Q}$

Using the discriminant to find Galois group of a quartic

How To Prove That The Rijndael Polynomial Is Irreducible?

what does $\alpha$ signify in finite fields modular arithmetic

Proof that $a^{n}+b^{n}$ is irreducible over $\mathbb Q$

Let $P$ $\in$ $\mathbb{F}_{p}[x,y]$, if $P$ does not have multiple factors then $P-1$ is irreducible.

Prove that $X^4+X^3+X^2+X+1$ is irreducible in $\mathbb{Q}[X]$, but that it has two different irreducible factors in $\mathbb{R}[X]$

Leading term ideal irreducible iff the ideal is irreducible?

Seeking an "easy " way to show that $p(x)=x^6+\cdots+x^2+x+1$ is irreducible over $\Bbb{Z_{17}}$

Knowing the Galois group of the splitting field of a polynomial $f$, how can I show that $f$ is irreducible in the ground field?

Show that $f(x)=x^3+(2+i)x+(1+i)$ is irreducible in $\mathbb{Z}[i][x]$

Give two polynomials in $\mathbb Q[x]$ (of degree 2 and 3) such that their product is an irreducible polynomial in $\mathbb Q[x]$ of degree 5

Is it possible to have a such polynomials?

Why are these two calculations in $GF(2^5)$ not equal

Question on splitting field and irreducible polynomials.

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