List questions from finite-fields

Published on 28 Mar 2026 - 19:39

513

Views

Number of square-free polynomials over a finite field - a combinatorial interpretation?

Published on 25 Mar 2026 - 17:39

331

Views

Irreducibility of a polynomial modulo infinitely many primes

Published on 25 Feb 2016 - 20:21

167

Views

Pictures of curves over finite fields with many points

Published on 27 Mar 2026 - 23:23

862

Views

Show that $\mathbb{F}_{p^2}$ has an 8th root of unity

Published on 27 Feb 2016 - 18:56

75

Views

Adjoining a root of $p$ to $F_p$ is etale?!

Published on 28 Feb 2016 - 11:33

68

Views

Analogue of orbit counting formula in $F[x]$

Published on 25 Mar 2026 - 19:05

66

Views

Find $n$ such that $f$ is reducible or give a proof.

Published on 28 Feb 2016 - 17:19

597

Views

How to write a given element of the orthogonal group as a product of reflections

Published on 09 Apr 2026 - 8:28

1k

Views

Question about finding smallest field given a primitive root of unity

Published on 10 Apr 2026 - 5:31

50

Views

maximum number of homogeneous linearly independent equation over $\mathbb{F}_{2^m}$

Published on 01 Apr 2026 - 16:45

60

Views

Showing that in $\mathbb{F}_q$, $q$ is odd, that $x^2=1$ has two solutions.

Published on 02 Mar 2016 - 7:17

152

Views

Proving $\mathbb{F}_p[x]/\langle f(x)\rangle$ with $f(x)$ irreducible is a finite field.

Published on 02 Mar 2016 - 8:28

52

Views

Galois: is $f(x)$ irreducible in $\mathbb{F}_5$

Published on 06 Apr 2026 - 16:37

5.3k

Views

Is $\mathbf{Z}[X]/(2,X^2+1)$ a field/PID?

Published on 30 Mar 2026 - 14:16

List Question

When is 2 a quadratic residue in a finite field?

Number of square-free polynomials over a finite field - a combinatorial interpretation?

Irreducibility of a polynomial modulo infinitely many primes

Pictures of curves over finite fields with many points

Show that $\mathbb{F}_{p^2}$ has an 8th root of unity

Adjoining a root of $p$ to $F_p$ is etale?!

Analogue of orbit counting formula in $F[x]$

Find $n$ such that $f$ is reducible or give a proof.

How to write a given element of the orthogonal group as a product of reflections

Question about finding smallest field given a primitive root of unity

maximum number of homogeneous linearly independent equation over $\mathbb{F}_{2^m}$

Showing that in $\mathbb{F}_q$, $q$ is odd, that $x^2=1$ has two solutions.

Proving $\mathbb{F}_p[x]/\langle f(x)\rangle$ with $f(x)$ irreducible is a finite field.

Galois: is $f(x)$ irreducible in $\mathbb{F}_5$

Is $\mathbf{Z}[X]/(2,X^2+1)$ a field/PID?

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