# Carmichael number

## Definition

A composite number  is termed an Carmichael number or absolute pseudoprime if it satisfies the following equivalent conditions:

1. The universal exponent (also called the Carmichael function)  of  divides .
2. For any natural number  relatively prime to ,  divides .
3.  is a Fermat pseudoprime to any base relatively prime to it.
4.  is a square-free odd number greater than 1 and  divides  for every prime divisor  of .