Question

Can every irreducible cubic be proved irreducible using the Eisenstein criterion?

score 219 · Answer 1 · 2017-04-16 04:48:31

219

Views

Can every irreducible cubic be proved irreducible using the Eisenstein criterion?

Published on 16 Apr 2017 - 4:48

score 58 · Answer 2 · 2017-04-16 06:22:05

58

Views

(Proof Verification) Prove that $f(x)$ is irreducible over $K$ implies it is irreducible over $F$.

Published on 16 Apr 2017 - 6:22

score 66 · Answer 3 · 2017-04-16 12:12:10

66

Views

Which of the following is a degree-100 extension of $\Bbb Q(i)$?

Published on 16 Apr 2017 - 12:12

score 295 · Answer 4 · 2017-04-17 05:13:34

295

Views

Find an example of degree-100 extension of $\Bbb Q(\zeta_5)$ and $\Bbb Q(\sqrt[3]{2})$.

Published on 17 Apr 2017 - 5:13

score 1.1k · Answer 5 · 2017-04-17 13:55:17

1.1k

Views

Direct and inverse limits of finite fields

Published on 17 Apr 2017 - 13:55

score 893 · Answer 6 · 2017-04-17 14:13:55

893

Views

Irreducible polynomial of degree 3

Published on 17 Apr 2017 - 14:13

score 582 · Answer 7 · 2017-04-17 15:18:41

582

Views

Is $x^{101} + 101x^{100} + 102$ irreducible?

Published on 17 Apr 2017 - 15:18

score 140 · Answer 8 · 2017-04-18 01:10:59

140

Views

What is the relationship between the minimal polynomial of $\alpha$ and the minimal polynomial of a linear function of $\alpha$?

Published on 18 Apr 2017 - 1:10

score 1.7k · Answer 9 · 2017-04-18 01:43:34

1.7k

Views

$6x^5+14x^3-21x+35$ is irreducible in $\mathbb{Q}[x]$

Published on 18 Apr 2017 - 1:43

score 223 · Answer 10 · 2017-04-18 08:04:49

223

Views

$x^{p-1}+x^{p-2}+\cdots+x+1$ is irreducible over $\mathbb{F}_2$ if and only if $2$ generates $\mathbb{F}_p^{*}$

Published on 18 Apr 2017 - 8:04

score 244 · Answer 11 · 2017-04-18 14:10:45

244

Views

$f(x)=x^4+ax^2+b\in \mathbb{Z}[x]$ is irreducible iff $\alpha ^2, \alpha \pm\beta$ are not elements of $\mathbb{Q}.$

Published on 18 Apr 2017 - 14:10

score 106 · Answer 12 · 2026-03-28 08:27:55

106

Views

Is $4x^2−1$ irreducible in $\mathbb{Z}[x]$?

Published on 28 Mar 2026 - 8:27

score 147 · Answer 13 · 2017-04-20 02:59:41

147

Views

If prime $p=a_n10^n+a_{n-1}10^{n-1}+\ldots+a_110+a_0$ then $f(x)=a_nx^n+\ldots+a_0$ is irreducible in $\mathbb{Z}[x]$

Published on 20 Apr 2017 - 2:59

score 1k · Answer 14 · 2017-04-20 05:40:41

1k

Views

The polynomial $f(x) = 2x^6 + 6x^5 + 4x^4 + 5x^3 + 3x +1 $ is irreducible in $\mathbb{Z}[x]$

Published on 20 Apr 2017 - 5:40

score 138 · Answer 15 · 2017-04-21 00:39:16

138

Views

Is the polynomial $x^2-xy^5-y^2-1$ an irreducible polynomial?

Published on 21 Apr 2017 - 0:39

List Question

Can every irreducible cubic be proved irreducible using the Eisenstein criterion?

(Proof Verification) Prove that $f(x)$ is irreducible over $K$ implies it is irreducible over $F$.

Which of the following is a degree-100 extension of $\Bbb Q(i)$?

Find an example of degree-100 extension of $\Bbb Q(\zeta_5)$ and $\Bbb Q(\sqrt[3]{2})$.

Direct and inverse limits of finite fields

Irreducible polynomial of degree 3

Is $x^{101} + 101x^{100} + 102$ irreducible?

What is the relationship between the minimal polynomial of $\alpha$ and the minimal polynomial of a linear function of $\alpha$?

$6x^5+14x^3-21x+35$ is irreducible in $\mathbb{Q}[x]$

$x^{p-1}+x^{p-2}+\cdots+x+1$ is irreducible over $\mathbb{F}_2$ if and only if $2$ generates $\mathbb{F}_p^{*}$

$f(x)=x^4+ax^2+b\in \mathbb{Z}[x]$ is irreducible iff $\alpha ^2, \alpha \pm\beta$ are not elements of $\mathbb{Q}.$

Is $4x^2−1$ irreducible in $\mathbb{Z}[x]$?

If prime $p=a_n10^n+a_{n-1}10^{n-1}+\ldots+a_110+a_0$ then $f(x)=a_nx^n+\ldots+a_0$ is irreducible in $\mathbb{Z}[x]$

The polynomial $f(x) = 2x^6 + 6x^5 + 4x^4 + 5x^3 + 3x +1 $ is irreducible in $\mathbb{Z}[x]$

Is the polynomial $x^2-xy^5-y^2-1$ an irreducible polynomial?

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