In number theory a Carmichael number is a composite positive integer , which satisfies the congruence for all integers which are relatively prime to . Being relatively prime means that they do not have common divisors, other than 1. Such numbers are named after Robert Carmichael.
All prime numbers satisfy for all integers which are relatively prime to . This has been proven by the famous mathematician Pierre de Fermat. In most cases if a number 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.