Question

Proof $27X^3 - 13X^2 + 180 \in \mathbb{Q}[x]$ is irreducible without Gauss's lemma

score 275 · Answer 1 · 2015-01-20 18:37:52

275

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Proof $27X^3 - 13X^2 + 180 \in \mathbb{Q}[x]$ is irreducible without Gauss's lemma

Published on 20 Jan 2015 - 18:37

score 167 · Answer 2 · 2015-01-20 18:54:26

167

Views

Elementary proof of the irreducibility of $T^4 - a T - 1$ in $\mathbf{Q}[T]$ when $a\in\mathbf{Z}-\{0\}$

Published on 20 Jan 2015 - 18:54

score 999 · Answer 3 · 2015-01-23 17:34:17

999

Views

A walkthrough of how to apply Eisenstein's criteria to show that a multivariate polynomial is irreductible.

Published on 23 Jan 2015 - 17:34

score 13.2k · Answer 4 · 2015-01-23 21:16:02

13.2k

Views

How do you show that the degree of an irreducible polynomial over the reals is either one or two?

Published on 23 Jan 2015 - 21:16

score 74 · Answer 5 · 2015-01-24 12:46:34

74

Views

Irreducibility of $x^4+x^3+x^2+x+1$

Published on 24 Jan 2015 - 12:46

score 1.2k · Answer 6 · 2015-01-24 13:07:25

1.2k

Views

Why is 105th cyclotomic polynomial interesting?

Published on 24 Jan 2015 - 13:07

score 91 · Answer 7 · 2015-01-25 12:00:11

91

Views

Irreducible Polynomial in $\mathbb{Q}[x]$

Published on 25 Jan 2015 - 12:00

score 411 · Answer 8 · 2015-01-27 15:47:57

411

Views

Efficient Computation of Swinnerton-Dyer Polynomials

Published on 27 Jan 2015 - 15:47

score 23 · Answer 9 · 2015-01-30 20:52:47

23

Views

$A \times B^{-1}$ has irreducible characteristic polynomial when $A,B$ are random integer matrices -- simple proof?

Published on 30 Jan 2015 - 20:52

score 276 · Answer 10 · 2015-02-01 14:58:51

276

Views

Find the irreducible polynomial of $\zeta_{12}$ and $\zeta_9$ over the field $Q(\zeta_3)$.

Published on 01 Feb 2015 - 14:58

score 1.6k · Answer 11 · 2015-02-02 08:21:15

1.6k

Views

If f and g are irreducible polynomials in K[X,Y ] that are not associates, show that the zero set Z(f,g) is either empty or finite

Published on 02 Feb 2015 - 8:21

score 811 · Answer 12 · 2015-02-02 13:41:36

811

Views

Proof of lemma about product of irreducible polynomials over finite fields

Published on 02 Feb 2015 - 13:41

score 3.3k · Answer 13 · 2015-02-03 03:25:38

3.3k

Views

The degree of $\sqrt{2} + \sqrt[3]{5}$ over $\mathbb Q$

Published on 03 Feb 2015 - 3:25

score 90 · Answer 14 · 2015-02-04 10:36:24

90

Views

Is $f(x,y)=7x-x^2y+2xy^3-x^3y^4+y^{100}\in F[x,y]$ irreducible.

Published on 04 Feb 2015 - 10:36

score 47 · Answer 15 · 2015-02-04 12:10:41

47

Views

irreduciblity in $\mathbb C[x,y,z]$

Published on 04 Feb 2015 - 12:10

List Question

Proof $27X^3 - 13X^2 + 180 \in \mathbb{Q}[x]$ is irreducible without Gauss's lemma

Elementary proof of the irreducibility of $T^4 - a T - 1$ in $\mathbf{Q}[T]$ when $a\in\mathbf{Z}-\{0\}$

A walkthrough of how to apply Eisenstein's criteria to show that a multivariate polynomial is irreductible.

How do you show that the degree of an irreducible polynomial over the reals is either one or two?

Irreducibility of $x^4+x^3+x^2+x+1$

Why is 105th cyclotomic polynomial interesting?

Irreducible Polynomial in $\mathbb{Q}[x]$

Efficient Computation of Swinnerton-Dyer Polynomials

$A \times B^{-1}$ has irreducible characteristic polynomial when $A,B$ are random integer matrices -- simple proof?

Find the irreducible polynomial of $\zeta_{12}$ and $\zeta_9$ over the field $Q(\zeta_3)$.

If f and g are irreducible polynomials in K[X,Y ] that are not associates, show that the zero set Z(f,g) is either empty or finite

Proof of lemma about product of irreducible polynomials over finite fields

The degree of $\sqrt{2} + \sqrt[3]{5}$ over $\mathbb Q$

Is $f(x,y)=7x-x^2y+2xy^3-x^3y^4+y^{100}\in F[x,y]$ irreducible.

irreduciblity in $\mathbb C[x,y,z]$

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