# Difference between revisions of "Fermat pseudoprime"

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

## 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

### 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).