Question

Solve $x^2+4=0$ in $\mathbb{F}_7[\sqrt{-1}]$

score 56 · Answer 1 · 2019-12-14 21:08:40

56

Views

Solve $x^2+4=0$ in $\mathbb{F}_7[\sqrt{-1}]$

Published on 14 Dec 2019 - 21:08

score 38 · Answer 2 · 2019-12-17 15:44:38

38

Views

$p$ is a prime number, $\, n\ge1 \, $and$ \, n \nmid p^n$.If $a \in GF(p)$, proof $x^{p^n}-x-a$ is reducible in $GF(p)$

Published on 17 Dec 2019 - 15:44

score 98 · Answer 3 · 2019-12-18 18:28:56

98

Views

Existence of a linearly independent subset in $\mathbb{Z}/p\mathbb{Z}$.

Published on 18 Dec 2019 - 18:28

score 783 · Answer 4 · 2026-03-26 12:58:12

783

Views

Product of Irreducible Polynomials

Published on 26 Mar 2026 - 12:58

score 58 · Answer 5 · 2019-12-21 09:01:46

58

Views

Construct a self-dual basis of $\Bbb F_{16}$ over $\Bbb F_2$

Published on 21 Dec 2019 - 9:01

score 32 · Answer 6 · 2026-03-30 01:15:16

32

Views

Number of products a * b giving a chosen value n in a finite field Fp

Published on 30 Mar 2026 - 1:15

score 137 · Answer 7 · 2019-12-21 13:19:57

137

Views

The equation $x^2+y^2=0$ over finite fields

Published on 21 Dec 2019 - 13:19

score 113 · Answer 8 · 2026-02-23 12:05:42

113

Views

Is the average multiplicative order of a finite field often small?

Published on 23 Feb 2026 - 12:05

score 35 · Answer 9 · 2026-03-26 14:34:54

35

Views

Let $F\supset F_p$ be a finite field extension. Prove that $F$ is a splitting extension.

Published on 26 Mar 2026 - 14:34

score 957 · Answer 10 · 2026-03-30 08:32:47

957

Views

Euler's phi function for polynomials over a finite field.

Published on 30 Mar 2026 - 8:32

score 60 · Answer 11 · 2026-02-23 08:41:32

60

Views

$g$-periodic points (related to periodicity of Chebyshev polynomials on finite fields)

Published on 23 Feb 2026 - 8:41

score 202 · Answer 12 · 2026-03-28 11:22:06

202

Views

Construct Galois field extension from a given a Galois Field

Published on 28 Mar 2026 - 11:22

score 66 · Answer 13 · 2019-12-30 00:23:42

66

Views

show that ${ x^4+x+1 \in GF(2^2)[x] }$

Published on 30 Dec 2019 - 0:23

score 1.4k · Answer 14 · 2019-12-30 11:05:56

1.4k

Views

How to find minimal polynomial on finite field ${ GF(2^4) }$

Published on 30 Dec 2019 - 11:05

score 669 · Answer 15 · 2019-12-30 12:11:01

669

Views

find minimal polynomial in ${GF(3^2)}$

Published on 30 Dec 2019 - 12:11

List Question

Solve $x^2+4=0$ in $\mathbb{F}_7[\sqrt{-1}]$

$p$ is a prime number, $\, n\ge1 \, $and$ \, n \nmid p^n$.If $a \in GF(p)$, proof $x^{p^n}-x-a$ is reducible in $GF(p)$

Existence of a linearly independent subset in $\mathbb{Z}/p\mathbb{Z}$.

Product of Irreducible Polynomials

Construct a self-dual basis of $\Bbb F_{16}$ over $\Bbb F_2$

Number of products a * b giving a chosen value n in a finite field Fp

The equation $x^2+y^2=0$ over finite fields

Is the average multiplicative order of a finite field often small?

Let $F\supset F_p$ be a finite field extension. Prove that $F$ is a splitting extension.

Euler's phi function for polynomials over a finite field.

$g$-periodic points (related to periodicity of Chebyshev polynomials on finite fields)

Construct Galois field extension from a given a Galois Field

show that ${ x^4+x+1 \in GF(2^2)[x] }$

How to find minimal polynomial on finite field ${ GF(2^4) }$

find minimal polynomial in ${GF(3^2)}$

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