# Fermat pseudoprime

From Number

Template:Base-relative pseudoprimality property
*This is not to be confused with Fermat prime*

## Contents

## Definition

Suppose is a composite natural number and is relatively prime to . is termed a **Fermat pseudoprime** relative to base if we have:

.

In other words, divides , or, the order of mod divides .

## Facts

## Relation with other properties

### Stronger properties

- Strong pseudoprime to a given base.
- Euler pseudoprime to a given base.
- Euler-Jacobi pseudoprime to a given base.

### Property when applied to one or more choice of base

- Carmichael number is a number that is a Fermat pseudoprime for every (relatively prime) base.
- Poulet number is a Fermat pseudoprime to base (in particular, it needs to be an odd number).