Question

how to prove $X+X^5+X^7$ in $F_{2^m}$ where $m \neq 0 \space \pmod 3$ is a permutation

score 86 · Answer 1 · 2026-04-15 21:00:13

86

Views

how to prove $X+X^5+X^7$ in $F_{2^m}$ where $m \neq 0 \space \pmod 3$ is a permutation

Published on 15 Apr 2026 - 21:00

score 132 · Answer 2 · 2026-04-17 06:19:30

132

Views

Proving a polynomial in $\mathbb{F}_p[x]$ is irreducible if and only if it is relatively prime to $x^{p^2}-x$.

Published on 17 Apr 2026 - 6:19

score 279 · Answer 3 · 2026-04-15 17:06:21

279

Views

Number of roots for a univariate polynomial in a finite field

Published on 15 Apr 2026 - 17:06

score 43 · Answer 4 · 2026-04-14 06:17:46

43

Views

$ p(x) $ as a product of irreducible (over $ \mathbb{F}$) factors.

Published on 14 Apr 2026 - 6:17

score 120 · Answer 5 · 2026-04-11 13:15:08

120

Views

Question about recursive formula for carry bit in modular addition mod $2^n$

Published on 11 Apr 2026 - 13:15

score 49 · Answer 6 · 2026-04-12 11:15:33

49

Views

How can $F^{\infty}$ be defined over a field F?

Published on 12 Apr 2026 - 11:15

score 67 · Answer 7 · 2026-04-14 03:39:32

67

Views

A Quick Question Concerning Iwasawa's Paper "On Galois Groups of Local Fields"

Published on 14 Apr 2026 - 3:39

score 67 · Answer 8 · 2026-04-17 12:22:16

67

Views

$F_{q^d}/F_q$ a finite field extension, a question about the homomorphism: $Aut_{F_q}(F_{q^d})\to Aut(F^{\times}_{q^d})$.

Published on 17 Apr 2026 - 12:22

score 350 · Answer 9 · 2026-04-13 23:31:37

350

Views

Gaussian Integers and Finite Fields

Published on 13 Apr 2026 - 23:31

score 546 · Answer 10 · 2026-05-04 09:02:45

546

Views

Let $K/F$ be a finite extension of finite fields and suppose $K=F[\alpha]$ with $\alpha^{15}=1$ then $\mid K:F \mid \leq 4$.

Published on 04 May 2026 - 9:02

score 265 · Answer 11 · 2026-05-04 10:01:14

265

Views

For $a,b \in \mathbb {F}_{{2^n}}$, $n$ is odd; $a^2+b^2+ab=0$ implies that $a=b=0$.

Published on 04 May 2026 - 10:01

score 74 · Answer 12 · 2026-04-17 23:18:53

74

Views

Determinant of matrix over $\mathbb{F}_{p}[x]$

Published on 17 Apr 2026 - 23:18

score 253 · Answer 13 · 2026-04-16 22:40:00

253

Views

Describing $\text{Spec}(\mathbb{F}_p[x])$

Published on 16 Apr 2026 - 22:40

score 167 · Answer 14 · 2026-04-16 23:32:18

167

Views

Find the irreducible decomposition of $x^{16}+x$ over $\mathbb{F_8}=\mathbb{F_2}[t]/(t^{3}+t+1)$.

Published on 16 Apr 2026 - 23:32

score 786 · Answer 15 · 2026-04-14 00:59:36

786

Views

Why must any finite field have a non-zero characteristic?

Published on 14 Apr 2026 - 0:59

List Question

how to prove $X+X^5+X^7$ in $F_{2^m}$ where $m \neq 0 \space \pmod 3$ is a permutation

Proving a polynomial in $\mathbb{F}_p[x]$ is irreducible if and only if it is relatively prime to $x^{p^2}-x$.

Number of roots for a univariate polynomial in a finite field

$ p(x) $ as a product of irreducible (over $ \mathbb{F}$) factors.

Question about recursive formula for carry bit in modular addition mod $2^n$

How can $F^{\infty}$ be defined over a field F?

A Quick Question Concerning Iwasawa's Paper "On Galois Groups of Local Fields"

$F_{q^d}/F_q$ a finite field extension, a question about the homomorphism: $Aut_{F_q}(F_{q^d})\to Aut(F^{\times}_{q^d})$.

Gaussian Integers and Finite Fields

Let $K/F$ be a finite extension of finite fields and suppose $K=F[\alpha]$ with $\alpha^{15}=1$ then $\mid K:F \mid \leq 4$.

For $a,b \in \mathbb {F}_{{2^n}}$, $n$ is odd; $a^2+b^2+ab=0$ implies that $a=b=0$.

Determinant of matrix over $\mathbb{F}_{p}[x]$

Describing $\text{Spec}(\mathbb{F}_p[x])$

Find the irreducible decomposition of $x^{16}+x$ over $\mathbb{F_8}=\mathbb{F_2}[t]/(t^{3}+t+1)$.

Why must any finite field have a non-zero characteristic?

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