Question

How to check if $x^{21} + 2x^8 + 1$ and $x^{21} + 2x^9 + 1$ are irreducible in $\mathbb{Z}_3$?

score 138 · Answer 1 · 2018-06-13 23:17:20

138

Views

How to check if $x^{21} + 2x^8 + 1$ and $x^{21} + 2x^9 + 1$ are irreducible in $\mathbb{Z}_3$?

Published on 13 Jun 2018 - 23:17

score 618 · Answer 2 · 2018-06-15 15:32:49

618

Views

For $p$ prime, is the polynomial $x^p-x+1$ irreducible in $\mathbb{Z}_p$?

Published on 15 Jun 2018 - 15:32

score 522 · Answer 3 · 2018-06-20 01:05:13

522

Views

Why is $F[x,y,z]/(x^2-yz)$ a domain?

Published on 20 Jun 2018 - 1:05

score 337 · Answer 4 · 2018-06-21 06:19:45

337

Views

What are the factors of this quotient given by Fermat's Little Theorem?

Published on 21 Jun 2018 - 6:19

score 525 · Answer 5 · 2018-06-23 08:48:24

525

Views

Irreducible polynomial is square-free modulo almost every prime

Published on 23 Jun 2018 - 8:48

score 1.1k · Answer 6 · 2018-06-24 18:20:47

1.1k

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Find all the monic irreducible polynomials of degree less than equal to $3$ in $F_2[X]$, and the same in $F_3[x]$.

Published on 24 Jun 2018 - 18:20

score 124 · Answer 7 · 2018-06-26 16:58:57

124

Views

Least degree polynomial with integer coefficient and having one root $\sqrt{8+\sqrt 6 +4\sqrt 3+ 3\sqrt 2}$

Published on 26 Jun 2018 - 16:58

score 784 · Answer 8 · 2018-06-26 19:47:50

784

Views

Is the ideal $I:=\langle xy-z,x^5-z^3 \rangle $ prime in $\Bbb{C}[x,y,z]$?

Published on 26 Jun 2018 - 19:47

score 539 · Answer 9 · 2026-03-25 04:43:50

539

Views

If the homomorphic image of a polynomial is irreducible, does it imply polynomial is irreducible

Published on 25 Mar 2026 - 4:43

score 118 · Answer 10 · 2018-06-28 04:01:09

118

Views

Homomorphism and irreducible polynomials

Published on 28 Jun 2018 - 4:01

score 72 · Answer 11 · 2026-03-25 04:38:52

72

Views

How can I show that irreducibility for this set?

Published on 25 Mar 2026 - 4:38

score 65 · Answer 12 · 2018-07-02 15:05:36

65

Views

Irreductibility of a polynom

Published on 02 Jul 2018 - 15:05

score 200 · Answer 13 · 2018-07-02 19:44:58

200

Views

Proving that the polynomial $10X^6-15X^2+7$ is irreducible in $\mathbb{Q}[X].$

Published on 02 Jul 2018 - 19:44

score 169 · Answer 14 · 2018-07-04 12:59:31

169

Views

Fastest way to factorize $x^{18}-x^3$ over $\mathbb{F}_2$

Published on 04 Jul 2018 - 12:59

score 192 · Answer 15 · 2018-07-06 03:07:10

192

Views

Is $f(x) = x^4 + x^2 + 1$ reducible in $\Bbb Z_2$?

Published on 06 Jul 2018 - 3:07

List Question

How to check if $x^{21} + 2x^8 + 1$ and $x^{21} + 2x^9 + 1$ are irreducible in $\mathbb{Z}_3$?

For $p$ prime, is the polynomial $x^p-x+1$ irreducible in $\mathbb{Z}_p$?

Why is $F[x,y,z]/(x^2-yz)$ a domain?

What are the factors of this quotient given by Fermat's Little Theorem?

Irreducible polynomial is square-free modulo almost every prime

Find all the monic irreducible polynomials of degree less than equal to $3$ in $F_2[X]$, and the same in $F_3[x]$.

Least degree polynomial with integer coefficient and having one root $\sqrt{8+\sqrt 6 +4\sqrt 3+ 3\sqrt 2}$

Is the ideal $I:=\langle xy-z,x^5-z^3 \rangle $ prime in $\Bbb{C}[x,y,z]$?

If the homomorphic image of a polynomial is irreducible, does it imply polynomial is irreducible

Homomorphism and irreducible polynomials

How can I show that irreducibility for this set?

Irreductibility of a polynom

Proving that the polynomial $10X^6-15X^2+7$ is irreducible in $\mathbb{Q}[X].$

Fastest way to factorize $x^{18}-x^3$ over $\mathbb{F}_2$

Is $f(x) = x^4 + x^2 + 1$ reducible in $\Bbb Z_2$?

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