New posts in finite-fields

Elementary proof that there is no field with 6 elements

abstract-algebra field-theory finite-fields alternative-proof

Derivations of Polynomial Algebra

abstract-algebra finite-fields

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

abstract-algebra field-theory finite-fields positive-characteristic

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

linear-algebra abstract-algebra finite-fields linear-groups

Pattern of Newton-Raphson iteration $x\mapsto\frac{1}{2}(x+\frac{q}{x})$ over finite fields

graph-theory finite-fields newton-raphson

Whats the probability a subset of an $\mathbb F_2$ vector space is a spanning set?

combinatorics reference-request finite-fields

Galois Field Fourier Transform

field-theory finite-fields coding-theory

Irreducibility of $x^{2n}+x^n+1$

field-theory finite-fields irreducible-polynomials

Why is the product of all units of a finite field equal to $-1$?

field-theory finite-fields

Why isn't the zero ring the field with one element?

algebraic-geometry field-theory finite-fields

Why are the elements of a galois/finite field represented as polynomials?

galois-theory finite-fields

Algorithm to find solution to $ax^2 + by^2 = 1$ in a finite field

elementary-number-theory finite-fields square-numbers sums-of-squares

Finding the values of $n$ for which $\mathbb{F}_{5^{n}}$, the finite field with $5^{n}$ elements, contains a non-trivial $93$rd root of unity

abstract-algebra finite-fields

Determine the degree of the splitting field for $f(x)=x^{15}-1$.

abstract-algebra field-theory finite-fields extension-field cyclotomic-polynomials

A *finite* first order theory whose finite models are exactly the $\Bbb F_p$?

logic field-theory finite-fields model-theory first-order-logic

Show the norm map is surjective

abstract-algebra galois-theory finite-fields

Field Norm Surjective for Finite Extensions of $\mathbb{F}_{p^k}$

field-theory galois-theory finite-fields

Fibonacci numbers mod $p$

prime-numbers modular-arithmetic finite-fields fibonacci-numbers

$p^{th}$ roots of a field with characteristic $p$

abstract-algebra field-theory finite-fields

Prove that the fields $\mathbb Z_{11}[x]/\langle x^2+1\rangle$ and $\mathbb Z_{11}[x]/\langle x^2+x+4 \rangle$ are isomorphic

abstract-algebra field-theory finite-fields