Difference between revisions of "Fermat pseudoprime"
From Number
(Created page with '{{base-relative pseudoprimality property}} ==Definition== Suppose <math>n</math> is a composite natural number and <math>a</math> is relatively prime to <math>n</math>. <math>n...') |
|||
| Line 1: | Line 1: | ||
{{base-relative pseudoprimality property}} | {{base-relative pseudoprimality property}} | ||
| − | + | {{nottobeconfusedwith|Fermat prime}} | |
==Definition== | ==Definition== | ||
Revision as of 22:26, 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
- Absolute pseudoprime 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).
