Question

$x^8-1$ - Irreductible polynomials over $\mathbb{Z}/3\mathbb{Z}$.

score 62 · Answer 1 · 2016-03-09 03:44:20

62

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$x^8-1$ - Irreductible polynomials over $\mathbb{Z}/3\mathbb{Z}$.

Published on 09 Mar 2016 - 3:44

score 381 · Answer 2 · 2016-03-09 23:35:29

381

Views

Show that the polynomial $x^3+nx+2$ is irreductible in $\mathbb{Z}[x]$ for all integers $n \in \mathbb{Z}-\{1,-3,-5\}$

Published on 09 Mar 2016 - 23:35

score 256 · Answer 3 · 2016-03-10 00:11:29

256

Views

Show that $p(x)=x^2-\sqrt{2}$ is irreductible on $\mathbb{Z}[\sqrt{2}]$

Published on 10 Mar 2016 - 0:11

score 476 · Answer 4 · 2016-03-10 01:34:11

476

Views

Show that the polynomial $x^2+y^2-1$ is irreducible over $\mathbb{Q}[x,y]$

Published on 10 Mar 2016 - 1:34

score 4.5k · Answer 5 · 2016-03-10 04:25:11

4.5k

Views

Show that the polynomial $(x-1)(x-2) \cdots (x-n)-1$ is irreducible on $\mathbb{Z}[x]$ for all $n \geq 1$

Published on 10 Mar 2016 - 4:25

score 722 · Answer 6 · 2026-03-28 05:23:11

722

Views

Degree of the splitting field of an irreducible polynomial of degree three

Published on 28 Mar 2026 - 5:23

score 112 · Answer 7 · 2016-03-11 19:15:35

112

Views

Variation on Perron's criterion

Published on 11 Mar 2016 - 19:15

score 382 · Answer 8 · 2026-03-26 08:03:40

382

Views

Are derivatives of geometric progressions all irreducible?

Published on 26 Mar 2026 - 8:03

score 905 · Answer 9 · 2016-03-12 00:56:40

905

Views

Understanding Proof of Eisenstein's Criterion

Published on 12 Mar 2016 - 0:56

score 1.3k · Answer 10 · 2016-03-12 19:15:01

1.3k

Views

Proof of irreducibility of $x^2+1$ over $\mathbb{Z}_p[x]$

Published on 12 Mar 2016 - 19:15

score 741 · Answer 11 · 2016-03-13 23:57:53

741

Views

Find Galois Group of cubic polynomial $f(x)=x^3+6x^2+9x+3$ over $\mathbb{Q}$

Published on 13 Mar 2016 - 23:57

score 141 · Answer 12 · 2026-03-29 07:37:32

141

Views

Is this polynomial irreducible? $f(x)=x^3-117x+53$

Published on 29 Mar 2026 - 7:37

score 319 · Answer 13 · 2016-03-14 09:30:09

319

Views

Zeroes of irreducible two variables polynomial which is reducible in algebraic closure

Published on 14 Mar 2016 - 9:30

score 2.9k · Answer 14 · 2016-03-16 07:06:59

2.9k

Views

Express $x^8-x$ as a product of irreducibles in $\Bbb Z_2[x]$

Published on 16 Mar 2016 - 7:06

score 1k · Answer 15 · 2016-03-16 07:27:01

1k

Views

Show irreducible polynomial by factorization in $\mathbb{F}_2[X]$ and $\mathbb{F}_3[X]$

Published on 16 Mar 2016 - 7:27

List Question

$x^8-1$ - Irreductible polynomials over $\mathbb{Z}/3\mathbb{Z}$.

Show that the polynomial $x^3+nx+2$ is irreductible in $\mathbb{Z}[x]$ for all integers $n \in \mathbb{Z}-\{1,-3,-5\}$

Show that $p(x)=x^2-\sqrt{2}$ is irreductible on $\mathbb{Z}[\sqrt{2}]$

Show that the polynomial $x^2+y^2-1$ is irreducible over $\mathbb{Q}[x,y]$

Show that the polynomial $(x-1)(x-2) \cdots (x-n)-1$ is irreducible on $\mathbb{Z}[x]$ for all $n \geq 1$

Degree of the splitting field of an irreducible polynomial of degree three

Variation on Perron's criterion

Are derivatives of geometric progressions all irreducible?

Understanding Proof of Eisenstein's Criterion

Proof of irreducibility of $x^2+1$ over $\mathbb{Z}_p[x]$

Find Galois Group of cubic polynomial $f(x)=x^3+6x^2+9x+3$ over $\mathbb{Q}$

Is this polynomial irreducible? $f(x)=x^3-117x+53$

Zeroes of irreducible two variables polynomial which is reducible in algebraic closure

Express $x^8-x$ as a product of irreducibles in $\Bbb Z_2[x]$

Show irreducible polynomial by factorization in $\mathbb{F}_2[X]$ and $\mathbb{F}_3[X]$

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