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.

Occurrence

Initial examples

561, 1105, 1729, 2465, [SHOW MORE]

2821, 6601, 8911, 10585, 15841, 29341, 41041, 46657, 52633, 62745, 63973, 75361, 101101, 115921, 126217, 162401, 172081, 188461, 252601, 278545, 294409, 314821, 334153, 340561, 399001, 410041, 449065, 488881, 512461

View list on OEIS

Facts

• There are infinitely many Carmichael numbers