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).