Carmichael number

Definition

A composite number $n>1$ is termed an Carmichael number or absolute pseudoprime if it satisfies the following condition:

• The universal exponent (also called the Carmichael function) $\lambda (n)$ of $n$ divides $n-1$.
• For any natural number $a$ relatively prime to $n$, $n$ divides $a^{n-1}-1$.
• $n$ is a Fermat pseudoprime to any base relatively prime to it.

Facts

• There are infinitely many Carmichael numbers