Fermat's little 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,

$a^p\equiv a(\mathrm{m}\mathrm{o}\mathrm{d}p),$

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

$a^{p-1}\equiv 1(\mathrm{m}\mathrm{o}\mathrm{d}p)$