Question

Show that the polynomial $F(x)=x^4-7$ is irreducible in $\mathbb{F}_5$

score 371 · Answer 1 · 2019-11-28 17:19:55

371

Views

Show that the polynomial $F(x)=x^4-7$ is irreducible in $\mathbb{F}_5$

Published on 28 Nov 2019 - 17:19

score 31 · Answer 2 · 2026-03-26 17:53:24

31

Views

If a case of the Bunyakovsky conjecture holds for degree-$n$ $p(x)$, does it hold for all degree-$n$ $f(x)$ satisfying the criterion?

Published on 26 Mar 2026 - 17:53

score 166 · Answer 3 · 2019-11-30 07:05:10

166

Views

Irreducible cubic polynomial in $\mathbb{Q}[x]$ has no roots in $\mathbb{Q}(\sqrt{2}, 5^{1/4})$

Published on 30 Nov 2019 - 7:05

score 981 · Answer 4 · 2019-12-01 03:27:38

981

Views

If quadratic or cubic polynomial $f$ has no roots, then $f$ is irreducible.

Published on 01 Dec 2019 - 3:27

score 2.9k · Answer 5 · 2019-12-02 05:32:43

2.9k

Views

Is the polynomial $(x^3 + 2x + 1)$ irreducible in $\mathbb{Z}_{3}[x]$?

Published on 02 Dec 2019 - 5:32

score 629 · Answer 6 · 2019-12-03 02:29:25

629

Views

Find a degree-4 polynomial in $\mathbb{Q}[x]$ that is not irreducible but also has no roots.

Published on 03 Dec 2019 - 2:29

score 36 · Answer 7 · 2019-12-04 18:00:02

36

Views

Question about polynomials with rational coefficients

Published on 04 Dec 2019 - 18:00

score 40 · Answer 8 · 2019-12-05 09:21:26

40

Views

Form of $P \in \mathbf{R}[X]$ such that $P(x) \geq 0$ for $x \in [-1, 1]$

Published on 05 Dec 2019 - 9:21

score 87 · Answer 9 · 2026-03-28 08:09:35

87

Views

Prime and maximal ideals of $\mathbb{C}[x,y]$.

Published on 28 Mar 2026 - 8:09

score 229 · Answer 10 · 2019-12-07 16:40:05

229

Views

Field $\mathbb F_2$, Reducible and irreducible polynomials

Published on 07 Dec 2019 - 16:40

score 110 · Answer 11 · 2026-03-25 01:28:50

110

Views

$f(t,x)$ irreducible, unsolvable over $\mathbb Q(t)$ such that its specialization $f(t_0,t)$ over $\mathbb Q$ is inseparable and (un)solvable.

Published on 25 Mar 2026 - 1:28

score 49 · Answer 12 · 2019-12-09 05:55:38

49

Views

The splitting field and the Galois group of an irreducible polynomial

Published on 09 Dec 2019 - 5:55

score 631 · Answer 13 · 2019-12-09 09:22:49

631

Views

Questions concerning method of finding irreducible polynomials in F_2[X].

Published on 09 Dec 2019 - 9:22

score 47 · Answer 14 · 2019-12-09 23:06:18

47

Views

What are the possible degrees for $\Bbb C[x]$

Published on 09 Dec 2019 - 23:06

score 1.2k · Answer 15 · 2019-12-09 23:28:14

1.2k

Views

Factor $x^5+x^4+1$ into irreducible polynomials in $Z_2$

Published on 09 Dec 2019 - 23:28

List Question

Show that the polynomial $F(x)=x^4-7$ is irreducible in $\mathbb{F}_5$

If a case of the Bunyakovsky conjecture holds for degree-$n$ $p(x)$, does it hold for all degree-$n$ $f(x)$ satisfying the criterion?

Irreducible cubic polynomial in $\mathbb{Q}[x]$ has no roots in $\mathbb{Q}(\sqrt{2}, 5^{1/4})$

If quadratic or cubic polynomial $f$ has no roots, then $f$ is irreducible.

Is the polynomial $(x^3 + 2x + 1)$ irreducible in $\mathbb{Z}_{3}[x]$?

Find a degree-4 polynomial in $\mathbb{Q}[x]$ that is not irreducible but also has no roots.

Question about polynomials with rational coefficients

Form of $P \in \mathbf{R}[X]$ such that $P(x) \geq 0$ for $x \in [-1, 1]$

Prime and maximal ideals of $\mathbb{C}[x,y]$.

Field $\mathbb F_2$, Reducible and irreducible polynomials

$f(t,x)$ irreducible, unsolvable over $\mathbb Q(t)$ such that its specialization $f(t_0,t)$ over $\mathbb Q$ is inseparable and (un)solvable.

The splitting field and the Galois group of an irreducible polynomial

Questions concerning method of finding irreducible polynomials in F_2[X].

What are the possible degrees for $\Bbb C[x]$

Factor $x^5+x^4+1$ into irreducible polynomials in $Z_2$

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