Carmichael number

In number theory a Carmichael number is a composite positive integer $n$, which satisfies the congruence $b^{n-1}\equiv 1{\pmod {n}}$ for all integers $b$ which are relatively prime to $n$. Being relatively prime means that they do not have common divisors, other than 1. Such numbers are named after Robert Carmichael.

All prime numbers $p$ satisfy $b^{p-1}\equiv 1{\pmod {p}}$ for all integers $b$ which are relatively prime to $p$. This has been proven by the famous mathematician Pierre de Fermat. In most cases if a number $n$ is composite, it does not satisfy this congruence equation. So, there exist not so many Carmichael numbers. We can say that Carmichael numbers are composite numbers that behave a little bit like they would be a prime number.