List questions from finite-fields

Published on 11 Jan 2016 - 6:58

187

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In the finite field $F$ of characteristic $p$, is $a^{p^n} = a$?

Published on 12 Jan 2016 - 15:03

200

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Finite geometry - how to determine parallel classes

Published on 25 Mar 2026 - 7:46

49

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Show that the set {${\alpha \in F_{5^6} | F_5(\alpha)=F_{5^6} }$} contains 15480 elements

Published on 12 Jan 2016 - 18:32

1.7k

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Monic irreducible polynomials of degree 6 in $F_{5}[X]$

Published on 06 Apr 2026 - 10:20

120

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$1+x+x^2 + \cdots + x^{p-1}$ in finite field

Published on 13 Jan 2016 - 6:48

83

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Finite Fields problem

Published on 15 Jan 2016 - 12:08

1k

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Splitting Field of the polynomial $x^4+x+1$ over $\mathbb{F}_2$.

Published on 28 Mar 2026 - 3:27

1.8k

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The equation $-1 = x^2 + y^2$ in finite fields

Published on 16 Jan 2016 - 18:11

370

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Isomorphic quotients of polynomial rings over finite fields

Published on 17 Jan 2016 - 9:57

312

Views

Relating a Character sum to a Gauss sum

Published on 28 Mar 2026 - 7:58

41

Views

A function in the integers module $p$ is polynomial.

Published on 18 Jan 2016 - 2:36

72

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Why the frobenius $\mathbb F_p^{alg}\longrightarrow \mathbb F_p^{alg}$ s.t. $x\longmapsto x^p$ is surjective?

Published on 18 Jan 2016 - 10:33

1.8k

Views

How can I get a irreducible polynomial of degree 8 over $Z_2[X]$?

Published on 06 Apr 2026 - 11:58

68

Views

How can we find $[GF(p^n):GF(p)]=n$?

Published on 18 Jan 2016 - 20:25

List Question

Are the following options correct in case of a field?

In the finite field $F$ of characteristic $p$, is $a^{p^n} = a$?

Finite geometry - how to determine parallel classes

Show that the set {${\alpha \in F_{5^6} | F_5(\alpha)=F_{5^6} }$} contains 15480 elements

Monic irreducible polynomials of degree 6 in $F_{5}[X]$

$1+x+x^2 + \cdots + x^{p-1}$ in finite field

Finite Fields problem

Splitting Field of the polynomial $x^4+x+1$ over $\mathbb{F}_2$.

The equation $-1 = x^2 + y^2$ in finite fields

Isomorphic quotients of polynomial rings over finite fields

Relating a Character sum to a Gauss sum

A function in the integers module $p$ is polynomial.

Why the frobenius $\mathbb F_p^{alg}\longrightarrow \mathbb F_p^{alg}$ s.t. $x\longmapsto x^p$ is surjective?

How can I get a irreducible polynomial of degree 8 over $Z_2[X]$?

How can we find $[GF(p^n):GF(p)]=n$?

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