Use this tag for questions about composite numbers n that satisfy b^(n-1) ≡ 1 (mod n) for all integers b relatively prime to n.
In number theory, a Carmichael number is a composite number n that satisfies the modular arithmetic congruence relation b$^{n-1}$ ≡ 1 (mod n) for all integers b relatively prime to n.
Fermat's little theorem states that if p is a prime number, then for any integer b, the number b$^p$ − b is an integer multiple of p. Carmichael numbers are composite numbers having that property. A Carmichael number will pass a Fermat primality test to every base b relatively prime to the number even though it is not actually prime. That makes tests based on Fermat's little theorem less effective than strong probable prime tests.
