Question

Showing $x^4+x^2+x+1$ irreducible over $\mathbb{Z_3}$

score 524 · Answer 1 · 2018-11-08 18:22:00

524

Views

Showing $x^4+x^2+x+1$ irreducible over $\mathbb{Z_3}$

Published on 08 Nov 2018 - 18:22

score 56 · Answer 2 · 2018-11-17 07:52:32

56

Views

Example of polynomial in two variables

Published on 17 Nov 2018 - 7:52

score 346 · Answer 3 · 2018-11-19 00:50:28

346

Views

Irreducibility of $x^4 + x^3 + 1$ over finite field $\mathbb{F}_{2^{a}}$, $1 \leq a \leq 6$

Published on 19 Nov 2018 - 0:50

score 115 · Answer 4 · 2018-11-20 17:28:54

115

Views

If $\deg\left(f\right) = \min\left(\left\{d \in \mathbb{N}^\times;\; f\vert X^{q^d} - X\right\}\right)\,$, then $f$ is irreducible.

Published on 20 Nov 2018 - 17:28

score 1.3k · Answer 5 · 2018-11-20 23:47:41

1.3k

Views

How to prove that $x^5-5$ is irreducible over $\mathbb Q(\sqrt 2, \sqrt[3] 3) $

Published on 20 Nov 2018 - 23:47

score 88 · Answer 6 · 2018-11-21 06:01:37

88

Views

Why we ignore the other elements of $F_{p^k}$ when we check if any element of it is a root of multiplicity greater than $1$ in $p(x)$ or not?

Published on 21 Nov 2018 - 6:01

score 40 · Answer 7 · 2018-11-21 10:32:25

40

Views

multiplication of polynomials in $\mathbb{F}_2[x]$

Published on 21 Nov 2018 - 10:32

score 102 · Answer 8 · 2018-11-21 14:40:50

102

Views

Can this algorithm be fixed?

Published on 21 Nov 2018 - 14:40

score 103 · Answer 9 · 2018-11-21 18:06:37

103

Views

Prove or disprove: $x^{p}+a$ is irreducible where $a\in \mathbb{Z}_{p}$.

Published on 21 Nov 2018 - 18:06

score 54 · Answer 10 · 2026-03-25 20:35:15

54

Views

Notation and interpretation of Polynomials in $\mathbb{F}_{p}[x]$

Published on 25 Mar 2026 - 20:35

score 71 · Answer 11 · 2018-11-22 02:43:23

71

Views

Strategies for finding $[\mathbb{Q} (\sqrt{2} + \sqrt{3}) : \mathbb{Q} ]$

Published on 22 Nov 2018 - 2:43

score 100 · Answer 12 · 2018-11-22 04:36:26

100

Views

Factorise the following p(x) as the product of a linear term and a quadratic polynomial with no real roots.

Published on 22 Nov 2018 - 4:36

score 26 · Answer 13 · 2026-03-25 21:48:40

26

Views

Irreducibility of a polynomial over Rationals with condition given on its coefficients.

Published on 25 Mar 2026 - 21:48

score 181 · Answer 14 · 2026-03-25 16:08:21

181

Views

Number of elements in the ideal of Ring.

Published on 25 Mar 2026 - 16:08

score 137 · Answer 15 · 2018-11-25 17:16:27

137

Views

Irreducible fatorization of $X^n-1$ in both the ring of polynomials with complex coefficients and real coefficients

Published on 25 Nov 2018 - 17:16

List Question

Showing $x^4+x^2+x+1$ irreducible over $\mathbb{Z_3}$

Example of polynomial in two variables

Irreducibility of $x^4 + x^3 + 1$ over finite field $\mathbb{F}_{2^{a}}$, $1 \leq a \leq 6$

If $\deg\left(f\right) = \min\left(\left\{d \in \mathbb{N}^\times;\; f\vert X^{q^d} - X\right\}\right)\,$, then $f$ is irreducible.

How to prove that $x^5-5$ is irreducible over $\mathbb Q(\sqrt 2, \sqrt[3] 3) $

Why we ignore the other elements of $F_{p^k}$ when we check if any element of it is a root of multiplicity greater than $1$ in $p(x)$ or not?

multiplication of polynomials in $\mathbb{F}_2[x]$

Can this algorithm be fixed?

Prove or disprove: $x^{p}+a$ is irreducible where $a\in \mathbb{Z}_{p}$.

Notation and interpretation of Polynomials in $\mathbb{F}_{p}[x]$

Strategies for finding $[\mathbb{Q} (\sqrt{2} + \sqrt{3}) : \mathbb{Q} ]$

Factorise the following p(x) as the product of a linear term and a quadratic polynomial with no real roots.

Irreducibility of a polynomial over Rationals with condition given on its coefficients.

Number of elements in the ideal of Ring.

Irreducible fatorization of $X^n-1$ in both the ring of polynomials with complex coefficients and real coefficients

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