# Finite field calculator

This tool allows you to carry out algebraic operations on elements of a finite field.

A finite field $K={𝔽}_{q}$ is a field with $q={p}^{n}$ elements, where $p$ is a prime number.

For the case where $n=1$, you can also use Numerical calculator.
First give the number of elements:
$q$ =
If $q$ is not prime (i.e., $n>1$), the elements of ${𝔽}_{q}$ must be described by a generator $x$ whose minimal polynomial $x$ over ${𝔽}_{p}$ is irreducible of degree $n$. In this case, you should define:
$P\left(x\right)$ =
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