Newbetuts

Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?

Proving that a Galois group $Gal(E/Q)$ is isomorphic to $\mathbb{F}_p^\times$

Problems with interesting, non-trivial analogues in finite fields

Irreductible polynomial on a finite field of degree as large as wanted [duplicate]

Let $\mathbb{F}_2 \cong \mathbb{Z}/2\mathbb{Z}$. Is $x^4+x^2+1$ irreducible in $\mathbb{F}_2[x]$?

Fix point of squaring numbers mod p

Cubic root of a polynomial to modulo of another polynomial

Algorithm to multiply nimbers

Find inverse of element in a binary field

Factorization of $x^8-x$ over $F_2$ and $F_4$

Constructing a finite field

Sum of $n$ integers from set of size $2n-1$ divides $n$

How to find the n-th root of a polynomial in a binary field?

Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements

$x^p-x \equiv x(x-1)(x-2)\cdots (x-(p-1))\,\pmod{\!p}$

Finite fields, existence of field of order $p^n$,proof help

New posts in finite-fields

Is $v=\ (r_i)^{-1}\cdot z $, a uniformly random value of a field?

When is $\mathbb{F}_p[x]/(x^2-2)\simeq\mathbb{F}_p[x]/(x^2-3)$ for small primes?

Roots of Artin-Schreier equation

Field with $125$ elements

Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?

Proving that a Galois group $Gal(E/Q)$ is isomorphic to $\mathbb{F}_p^\times$

Problems with interesting, non-trivial analogues in finite fields

Irreductible polynomial on a finite field of degree as large as wanted [duplicate]

Let $\mathbb{F}_2 \cong \mathbb{Z}/2\mathbb{Z}$. Is $x^4+x^2+1$ irreducible in $\mathbb{F}_2[x]$?

Fix point of squaring numbers mod p

Cubic root of a polynomial to modulo of another polynomial

Algorithm to multiply nimbers

Find inverse of element in a binary field

Factorization of $x^8-x$ over $F_2$ and $F_4$

Constructing a finite field

Sum of $n$ integers from set of size $2n-1$ divides $n$

How to find the n-th root of a polynomial in a binary field?

Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements

$x^p-x \equiv x(x-1)(x-2)\cdots (x-(p-1))\,\pmod{\!p}$

Finite fields, existence of field of order $p^n$,proof help