New posts in Finite Fields

What do the elements of the field $\mathbb{Z}_2[x]/(x^4+x+1)$ look like? What is its order?

Let F be a field of order 32. Show that the only subfields of F are F itself and {0,1}.

A field is finite if and only if its multiplicative group is finitely generated.

Why is the multiplicative group of a finite field cyclic?

Sum of the values of a polynomial over a finite field

$GL_n(\mathbb F_q)$ has an element of order $q^n-1$

Galois group of algebraic closure of a finite field

How many irreducible monic quadratic polynomials are there in $\mathbb{F}_p[X]$?

On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$

Show that $f(x) = x^p -x -1 \in \Bbb{F}_p[x]$ is irreducible over $\Bbb{F}_p$ for every $p$.