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# Can anyone explain Fermats little theorem ?

Aman Bansal
592 Points
9 years ago

Dear Sathyaram,

Fermats little theorem (so named to distinguish it from Fermats last theorem) states that if p is a prime number, then for any integer aa p − a will be evenly divisible by p. This can be expressed in the notation of modular arithmetic as follows:

$a^p \equiv a \pmod{p}.\,\!$

A variant of this theorem is stated in the following form: if p is a prime and a is an integer coprime to p, then a p−1 − 1 will be evenly divisible by p. In the notation of modular arithmetic:

$a^{p-1} \equiv 1 \pmod{p}.\,\!$

Fermats little theorem is the basis for the Fermat primality test. The theorem is named after Pierre de Fermat.

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