# Fermat's little theorem

mathematics theorem

Fermat's little theorem is a theorem from number theory. It is named after Pierre de Fermat who found it in the 17th century. It is about the properties of primes. It says that if a is a number, and p is a prime number, then in the notation of modular Arithmetic, it can be expressed as,

${\displaystyle a^{p}\equiv a\,(\mathrm {mod} \,p),}$

If a is not a multiple of p, then the following is often used:

${\displaystyle a^{p-1}\equiv 1\,(\mathrm {mod} \,p)}$