List questions from finite-fields

Published on 29 Mar 2026 - 9:11

69

Views

Find the number of integers $r$ such that the polynomial $x^{r}-a$ has a linear factor over $\mathbb{F}_{p^{n}}$

Published on 06 Dec 2014 - 18:46

912

Views

Solvability of Artin-Schreier Polynomial

Published on 28 Mar 2026 - 15:26

300

Views

Does $SL(2, \mathbb F_p)$ always have a subgroup of order $(p-1)(p+1)$?

Published on 08 Dec 2014 - 20:47

329

Views

Finite field such that for every $a \in F$ , $x^2=a$ has a solution for $ x \in F$

Published on 09 Dec 2014 - 4:26

190

Views

Fixed point of field automorphism

Published on 11 Dec 2014 - 13:24

2.4k

Views

Why can a matrix whose kth power is I be diagonalized?

Published on 12 Dec 2014 - 2:05

216

Views

Subfield of a Field

Published on 12 Dec 2014 - 2:08

2.7k

Views

Infinite algebraic extension of a finite field

Published on 12 Dec 2014 - 19:52

37

Views

General construction of $\operatorname{GF}(2^k)$

Published on 12 Dec 2014 - 21:08

245

Views

Splitting field of $X^6-7X^4+3X^2+3$ over $\mathbb Q$ and $\mathbb F_{13}$

Published on 26 Mar 2026 - 8:23

45

Views

Cyclotomic extension of $\mathbb{F}_p((T))$

Published on 12 Dec 2014 - 22:40

742

Views

Order of $\mathrm{GL}_n(\mathbb F_p)$ for $p$ prime

Published on 15 Dec 2014 - 13:34

238

Views

When is a number square in Galois field $p^n$ if it's not square mod $p$?

Published on 17 Dec 2014 - 1:58

502

Views

Bounds for general character sums over finite fields

Published on 25 Mar 2026 - 13:42

List Question

Calculating of genus of a curve

Find the number of integers $r$ such that the polynomial $x^{r}-a$ has a linear factor over $\mathbb{F}_{p^{n}}$

Solvability of Artin-Schreier Polynomial

Does $SL(2, \mathbb F_p)$ always have a subgroup of order $(p-1)(p+1)$?

Finite field such that for every $a \in F$ , $x^2=a$ has a solution for $ x \in F$

Fixed point of field automorphism

Why can a matrix whose kth power is I be diagonalized?

Subfield of a Field

Infinite algebraic extension of a finite field

General construction of $\operatorname{GF}(2^k)$

Splitting field of $X^6-7X^4+3X^2+3$ over $\mathbb Q$ and $\mathbb F_{13}$

Cyclotomic extension of $\mathbb{F}_p((T))$

Order of $\mathrm{GL}_n(\mathbb F_p)$ for $p$ prime

When is a number square in Galois field $p^n$ if it's not square mod $p$?

Bounds for general character sums over finite fields

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