Fermat's little theorem is a fundamental theorem in number theory that states that if p is a prime number, then for any integer a, the number a^p - a is always a multiple of p.
Fermat's little theorem is a powerful tool in number theory and is often used in cryptography and primality testing. It also has applications in other areas of mathematics such as combinatorics and algebra.
No, Fermat's little theorem only holds true for prime moduli. There is a generalization of this theorem known as Euler's theorem which applies to any modulus and is based on the totient function.
It is called "little" theorem to distinguish it from Fermat's last theorem, which is a much more famous and difficult theorem. Fermat's little theorem is also considered "little" because of its simple and elegant proof compared to other theorems in number theory.
Fermat's little theorem was first stated by French mathematician Pierre de Fermat in the 17th century. However, it was not proven until much later by Swiss mathematician Leonhard Euler in the 18th century.