Question

Show that the field $L = \mathbb F_3[X]/\langle X^5 - X + 1\rangle$ consists of $243$ elements and that $[X][f] = [1]$ for some $[f] \in L$.

score 135 · Answer 1 · 2026-04-17 04:42:44

135

Views

Show that the field $L = \mathbb F_3[X]/\langle X^5 - X + 1\rangle$ consists of $243$ elements and that $[X][f] = [1]$ for some $[f] \in L$.

Published on 17 Apr 2026 - 4:42

score 71 · Answer 2 · 2026-04-10 02:13:49

71

Views

The BOOK proof of the quadratic reciprocity law - need explanation about prime field of finite field

Published on 10 Apr 2026 - 2:13

score 573 · Answer 3 · 2026-04-16 13:17:03

573

Views

finding fixed points of frobenius endomorphism of a ring of char > $p$ (not a domain)

Published on 16 Apr 2026 - 13:17

score 120 · Answer 4 · 2026-04-16 17:59:46

120

Views

Let $L = \mathbb F_2[X]/\langle X^4 + X + 1 \rangle$ is a field. Show $L^* = L / \{0\} = \langle X \rangle$ is cyclic.

Published on 16 Apr 2026 - 17:59

score 101 · Answer 5 · 2026-04-11 17:57:45

101

Views

Show irreducibilty over a finite field

Published on 11 Apr 2026 - 17:57

score 126 · Answer 6 · 2026-04-15 21:44:07

126

Views

Number of solutions of $x^m \neq y^m$, $z^n=w^n=t^n$ over a finite field.

Published on 15 Apr 2026 - 21:44

score 4.6k · Answer 7 · 2026-04-15 13:51:20

4.6k

Views

The trace map in a finite field.

Published on 15 Apr 2026 - 13:51

score 173 · Answer 8 · 2026-04-17 01:41:16

173

Views

The equation $y^p-y = x$ in finite fields.

Published on 17 Apr 2026 - 1:41

score 308 · Answer 9 · 2026-04-10 09:32:25

308

Views

Addition in finite fields

Published on 10 Apr 2026 - 9:32

score 469 · Answer 10 · 2026-04-11 04:35:39

469

Views

Finite Fields: Linear Feedback Shift Register Algorithm Help

Published on 11 Apr 2026 - 4:35

score 6.1k · Answer 11 · 2026-04-12 13:38:06

6.1k

Views

Galois group of algebraic closure of a finite field

Published on 12 Apr 2026 - 13:38

score 1.3k · Answer 12 · 2026-04-14 17:11:21

1.3k

Views

polynomials factorization over rings and finite fields

Published on 14 Apr 2026 - 17:11

score 206 · Answer 13 · 2026-04-12 16:03:55

206

Views

What is the smallest Finite Field in which the following polynomial is factorizable to irreducible factors?

Published on 12 Apr 2026 - 16:03

score 84 · Answer 14 · 2026-04-15 21:19:15

84

Views

Compute $a(x)b(x)+c(x)$ in $\mathrm{GF}(2^4)$ where the irreducible generator polynomial $x^4+x+1$.

Published on 15 Apr 2026 - 21:19

score 149 · Answer 15 · 2026-04-16 00:41:39

149

Views

Irreducible polynomials of degree $d$ such that $[x]$ generates $\mathbf{F}_{p^d}^{\times}$

Published on 16 Apr 2026 - 0:41

List Question

Show that the field $L = \mathbb F_3[X]/\langle X^5 - X + 1\rangle$ consists of $243$ elements and that $[X][f] = [1]$ for some $[f] \in L$.

The BOOK proof of the quadratic reciprocity law - need explanation about prime field of finite field

finding fixed points of frobenius endomorphism of a ring of char > $p$ (not a domain)

Let $L = \mathbb F_2[X]/\langle X^4 + X + 1 \rangle$ is a field. Show $L^* = L / \{0\} = \langle X \rangle$ is cyclic.

Show irreducibilty over a finite field

Number of solutions of $x^m \neq y^m$, $z^n=w^n=t^n$ over a finite field.

The trace map in a finite field.

The equation $y^p-y = x$ in finite fields.

Addition in finite fields

Finite Fields: Linear Feedback Shift Register Algorithm Help

Galois group of algebraic closure of a finite field

polynomials factorization over rings and finite fields

What is the smallest Finite Field in which the following polynomial is factorizable to irreducible factors?

Compute $a(x)b(x)+c(x)$ in $\mathrm{GF}(2^4)$ where the irreducible generator polynomial $x^4+x+1$.

Irreducible polynomials of degree $d$ such that $[x]$ generates $\mathbf{F}_{p^d}^{\times}$

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