Question

primitive polynomial and irreducible

score 369 · Answer 1 · 2020-04-21 15:23:17

369

Views

primitive polynomial and irreducible

Published on 21 Apr 2020 - 15:23

score 130 · Answer 2 · 2020-04-22 10:31:13

130

Views

Determine the number of irreducible polynomials of degrees 2, 3, and 6 over the prime ﬁeld $\mathbb F_p$.

Published on 22 Apr 2020 - 10:31

score 215 · Answer 3 · 2020-04-22 23:32:54

215

Views

Show that $Q(x):=200x^3-200x^2+200x+100$ is an irreducible polynomial over the field $\mathbb{Q}$ of rational numbers.

Published on 22 Apr 2020 - 23:32

score 127 · Answer 4 · 2020-04-22 23:50:49

127

Views

Finding Relationship Between Galois Conjugates

Published on 22 Apr 2020 - 23:50

score 106 · Answer 5 · 2020-04-23 00:02:18

106

Views

Show that as a polynomial in $\mathbb{Q}[x]$, $P(x)$ is irreducible.

Published on 23 Apr 2020 - 0:02

score 201 · Answer 6 · 2020-04-23 15:44:06

201

Views

How to show that $x^9-3$ is irreducible over $\mathbb Q\Big(\exp\left(\frac{2\pi i}5\right)\Big)$?

Published on 23 Apr 2020 - 15:44

score 203 · Answer 7 · 2020-04-23 15:51:09

203

Views

Prove $x^{p^k}-a$ is irreducible in a field $K$ of characteristic $p>0$ for all $k \geq 0$, where $a$ is not a $p^{th}$ power in $K$.

Published on 23 Apr 2020 - 15:51

score 38 · Answer 8 · 2020-04-23 17:32:43

38

Views

Eisenstein Criterion to verify a that a polynomial is irreducible

Published on 23 Apr 2020 - 17:32

score 95 · Answer 9 · 2026-03-26 01:23:39

95

Views

Determine the number of irreducible polynomials of degrees 2, 3, and 6 over a prime ﬁeld.

Published on 26 Mar 2026 - 1:23

score 703 · Answer 10 · 2020-04-26 01:59:37

703

Views

Show that $x^3 + 3x+2$ is irreducible in $\mathbb{Z}[5]$

Published on 26 Apr 2020 - 1:59

score 242 · Answer 11 · 2026-03-26 22:55:45

242

Views

Show that no root of the polynomial $x^5 + 21x^4 - 14x^3 + 28x^2 - 7x + 42$ is constructible.

Published on 26 Mar 2026 - 22:55

score 109 · Answer 12 · 2026-03-26 07:58:24

109

Views

Are the ring $\mathbb{R}[x]/(x^{2})$ and $\mathbb{R}[x]/(x^{3})$ isomorphic?

Published on 26 Mar 2026 - 7:58

score 73 · Answer 13 · 2020-04-27 16:32:14

73

Views

Prove non-constant, irreducible polynomials are primitive

Published on 27 Apr 2020 - 16:32

score 396 · Answer 14 · 2020-04-27 19:40:43

396

Views

The Galois group of polynomial $p(x)\in\mathbb{K}[x]$ is cyclic and is generated by $q(x)\in\mathbb{K}[x]$.

Published on 27 Apr 2020 - 19:40

score 182 · Answer 15 · 2020-04-28 07:18:05

182

Views

Is there an irreducible polynomial which cannot be judged by Eisenstein criterion

Published on 28 Apr 2020 - 7:18

List Question

primitive polynomial and irreducible

Determine the number of irreducible polynomials of degrees 2, 3, and 6 over the prime ﬁeld $\mathbb F_p$.

Show that $Q(x):=200x^3-200x^2+200x+100$ is an irreducible polynomial over the field $\mathbb{Q}$ of rational numbers.

Finding Relationship Between Galois Conjugates

Show that as a polynomial in $\mathbb{Q}[x]$, $P(x)$ is irreducible.

How to show that $x^9-3$ is irreducible over $\mathbb Q\Big(\exp\left(\frac{2\pi i}5\right)\Big)$?

Prove $x^{p^k}-a$ is irreducible in a field $K$ of characteristic $p>0$ for all $k \geq 0$, where $a$ is not a $p^{th}$ power in $K$.

Eisenstein Criterion to verify a that a polynomial is irreducible

Determine the number of irreducible polynomials of degrees 2, 3, and 6 over a prime ﬁeld.

Show that $x^3 + 3x+2$ is irreducible in $\mathbb{Z}[5]$

Show that no root of the polynomial $x^5 + 21x^4 - 14x^3 + 28x^2 - 7x + 42$ is constructible.

Are the ring $\mathbb{R}[x]/(x^{2})$ and $\mathbb{R}[x]/(x^{3})$ isomorphic?

Prove non-constant, irreducible polynomials are primitive

The Galois group of polynomial $p(x)\in\mathbb{K}[x]$ is cyclic and is generated by $q(x)\in\mathbb{K}[x]$.

Is there an irreducible polynomial which cannot be judged by Eisenstein criterion

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