# Frobenius Pseudoprimes

## TL;DR

This paper unifies various pseudoprime tests under a general framework using finite fields, aiming to develop stronger tests and facilitate proofs about large classes of pseudoprimes.

## Contribution

It introduces a unified theory of pseudoprimes, reformulating many tests within finite fields to enhance test strength and theoretical understanding.

## Key findings

- Unified framework for pseudoprimes using finite fields
- Reformulation enables stronger primality tests
- Facilitates proofs for large classes of pseudoprimes

## Abstract

The proliferation of probable prime tests in recent years has produced a plethora of definitions with the word ``pseudoprime'' in them. Examples include pseudoprimes, Euler pseudoprimes, strong pseudoprimes, Lucas pseudoprimes, strong Lucas pseudoprimes, extra strong Lucas pseudoprimes and Perrin pseudoprimes. Though these tests represent a wealth of ideas, they exist as a hodge-podge of definitions rather than as examples of a more general theory. It is the goal of this paper to present a way of viewing many of these tests as special cases of a general principle, as well as to re-formulate them in the context of finite fields. One aim of the reformulation is to enable the creations of stronger tests; another is to aid in proving results about large classes of pseudoprimes.