A Carmichael number is a composite number \( n \) that satisfies Fermat's little theorem for all integers \( a \) that are coprime to \( n \). Specifically, Fermat's little theorem states that if \( p \) is a prime number, then for any integer \( a \) such that \( a \) is not divisible by \( p \), \[ a^{p-1} \equiv 1 \ (\text{mod} \ p).
