Question

Factorizing multivariate polynomials in $GF_2[x_1, ..., x_n]/[x_1+x_1^2,...]$

score 100 · Answer 1 · 2026-03-25 20:35:24

100

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Factorizing multivariate polynomials in $GF_2[x_1, ..., x_n]/[x_1+x_1^2,...]$

Published on 25 Mar 2026 - 20:35

score 253 · Answer 2 · 2026-04-14 17:04:57

253

Views

$x^m-1 \nmid f(x)$ in $\mathbb{Z}/p\mathbb{Z}[x]$ where $f(x)=(x+1)((x+1)^{2m}+(x+1)^{m}+1)$

Published on 14 Apr 2026 - 17:04

score 172 · Answer 3 · 2026-04-14 08:55:52

172

Views

Interchanging field axioms on finite set

Published on 14 Apr 2026 - 8:55

score 110 · Answer 4 · 2026-04-16 00:45:04

110

Views

For a prime $p>3$, if $1+\frac{1}{2}+\cdots+\frac{1}{p-1}=\frac{a}{b}$, then $p^2 \mid a$.

Published on 16 Apr 2026 - 0:45

score 38 · Answer 5 · 2026-04-11 02:55:52

38

Views

Software to solve system equations over finite field extension.

Published on 11 Apr 2026 - 2:55

score 596 · Answer 6 · 2026-04-14 16:46:58

596

Views

sagemath GF(p^n) calculations

Published on 14 Apr 2026 - 16:46

score 490 · Answer 7 · 2026-04-11 12:41:36

490

Views

What does "underlying field" mean in the context of groups?

Published on 11 Apr 2026 - 12:41

score 52 · Answer 8 · 2026-04-16 13:00:12

52

Views

If $F$ is a field $a\in F$, if $(x-a)^n$ for $n\geq 2$ divides $r(x)$ then $r(a)=r^{\prime}(a)=0$

Published on 16 Apr 2026 - 13:00

score 48 · Answer 9 · 2026-04-09 14:43:29

48

Views

Understanding distribution of permutations defined by elements in finite fields

Published on 09 Apr 2026 - 14:43

score 86 · Answer 10 · 2026-04-16 02:17:09

86

Views

Number of matrices X^2 = 0 over F_q?

Published on 16 Apr 2026 - 2:17

score 260 · Answer 11 · 2026-04-17 06:46:01

260

Views

$X^2 +X +1$ is reducible in $\mathbb{F}_p [X]$ iff $p\equiv 1$ (mod 3)

Published on 17 Apr 2026 - 6:46

score 58 · Answer 12 · 2026-04-13 20:10:23

58

Views

Is $K=F_q^2\setminus V(f)$ is a Kakeya set in $F_q^2$?

Published on 13 Apr 2026 - 20:10

score 58 · Answer 13 · 2026-04-17 03:35:13

58

Views

Cardinality of $A_n=\{ x \in \mathbb{F}_{5}^{n} : x\cdot x=0\}$

Published on 17 Apr 2026 - 3:35

score 82 · Answer 14 · 2026-04-13 12:19:52

82

Views

Isomorphism between subgroups of $S_p$ and $GL_2(\mathbb{Z}/ p\mathbb{Z})$

Published on 13 Apr 2026 - 12:19

score 66 · Answer 15 · 2026-04-16 12:29:44

66

Views

Let $f(x)\in \Bbb{F}_p[x]$ be an irreducible polynomial of degree $m$, what is the number of irreducible factors of $f(x)$ in $\Bbb{F}_{p^n}[x]$?

Published on 16 Apr 2026 - 12:29

List Question

Factorizing multivariate polynomials in $GF_2[x_1, ..., x_n]/[x_1+x_1^2,...]$

$x^m-1 \nmid f(x)$ in $\mathbb{Z}/p\mathbb{Z}[x]$ where $f(x)=(x+1)((x+1)^{2m}+(x+1)^{m}+1)$

Interchanging field axioms on finite set

For a prime $p>3$, if $1+\frac{1}{2}+\cdots+\frac{1}{p-1}=\frac{a}{b}$, then $p^2 \mid a$.

Software to solve system equations over finite field extension.

sagemath GF(p^n) calculations

What does "underlying field" mean in the context of groups?

If $F$ is a field $a\in F$, if $(x-a)^n$ for $n\geq 2$ divides $r(x)$ then $r(a)=r^{\prime}(a)=0$

Understanding distribution of permutations defined by elements in finite fields

Number of matrices X^2 = 0 over F_q?

$X^2 +X +1$ is reducible in $\mathbb{F}_p [X]$ iff $p\equiv 1$ (mod 3)

Is $K=F_q^2\setminus V(f)$ is a Kakeya set in $F_q^2$?

Cardinality of $A_n=\{ x \in \mathbb{F}_{5}^{n} : x\cdot x=0\}$

Isomorphism between subgroups of $S_p$ and $GL_2(\mathbb{Z}/ p\mathbb{Z})$

Let $f(x)\in \Bbb{F}_p[x]$ be an irreducible polynomial of degree $m$, what is the number of irreducible factors of $f(x)$ in $\Bbb{F}_{p^n}[x]$?

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