List questions from finite-fields

Published on 23 Apr 2019 - 21:40

285

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How many elements of have square roots in a field of 13 elements?

Published on 25 Apr 2019 - 11:10

252

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How many solutions of the equation $ax^2 +by^2 = 1$ are there with $(x, y) ∈ \mathbb{F}_{p} ×\mathbb{F}_{p}$

Published on 25 Apr 2019 - 12:59

118

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$\mathbb{F}_p({\rm i}) = \mathbb{F}_{p^2}$ iff $p=3\mod 4$

Published on 26 Apr 2019 - 12:14

209

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Polynomial evaluates to quadratic residue in $p$ cases

Published on 25 Mar 2026 - 9:38

64

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Order of the splitting field of $f(x)$ with $\deg f(x)=11$ over $\Bbb F_p$?

Published on 28 Apr 2019 - 11:20

59

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A confusion on simple extension of a root of irreducible polynomial over a finite field

Published on 28 Apr 2019 - 12:57

72

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Catalan's conjecture in $\mathbb F_p$

Published on 28 Apr 2019 - 16:46

247

Views

Identity of Polynomials in positive charcteristic

Published on 29 Apr 2019 - 13:15

117

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Subgroup of finite field is invariant under Frobenius map

Published on 27 Mar 2026 - 22:12

129

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Isomorphism of fields via the forgetful functor

Published on 29 Apr 2019 - 15:48

689

Views

This matrix is diagonalizable over algebraic closure of $\Bbb F_p$ iff $(n,p)=1$

Published on 28 Mar 2026 - 1:02

182

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Isomorphisms between finite fields

Published on 26 Mar 2026 - 2:51

436

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Galois group of $F_{p^2}$ over $\mathbb{Z}_p$

Published on 30 Apr 2019 - 17:44

52

Views

Help understanding the question

Published on 30 Apr 2019 - 23:50

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proving $x$ is the generator of a cyclic group

How many elements of have square roots in a field of 13 elements?

How many solutions of the equation $ax^2 +by^2 = 1$ are there with $(x, y) ∈ \mathbb{F}_{p} ×\mathbb{F}_{p}$

$\mathbb{F}_p({\rm i}) = \mathbb{F}_{p^2}$ iff $p=3\mod 4$

Polynomial evaluates to quadratic residue in $p$ cases

Order of the splitting field of $f(x)$ with $\deg f(x)=11$ over $\Bbb F_p$?

A confusion on simple extension of a root of irreducible polynomial over a finite field

Catalan's conjecture in $\mathbb F_p$

Identity of Polynomials in positive charcteristic

Subgroup of finite field is invariant under Frobenius map

Isomorphism of fields via the forgetful functor

This matrix is diagonalizable over algebraic closure of $\Bbb F_p$ iff $(n,p)=1$

Isomorphisms between finite fields

Galois group of $F_{p^2}$ over $\mathbb{Z}_p$

Help understanding the question

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