Fermat's Little Theorem

Statement

If ${a}$ is an integer and ${p}$ is a prime number, then $a^{p-1}\equiv 1 \pmod {p}$ .

Note: This theorem is a special case of Euler's totient theorem.

Corollary

A frequently used corolary of Fermat's little theorem is $a^p \equiv a \pmod {p}$ . As you can see, it is derived by multipling both sides of the theorem by a.

Credit

This theorem is credited to Pierre Fermat.

Page

Toolbox

Search

Fermat's Little Theorem

Contents

Statement

Corollary

Credit

See also