# Difference between revisions of "Fermat pseudoprime"

From Number

(→Property when applied to one or more choice of base) |
|||

Line 19: | Line 19: | ||

===Property when applied to one or more choice of 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 <math>2</math> (in particular, it needs to be an odd number). | * [[Poulet number]] is a Fermat pseudoprime to base <math>2</math> (in particular, it needs to be an odd number). |

## Revision as of 22:28, 19 April 2009

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 .

## 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).