# Definition:Fermat Quotient

## Definition

Let $a$ be a positive integer.

Let $p$ be an odd prime.

The Fermat quotient of $a$ with respect to $p$ is defined as:

$\map {q_p} a = \dfrac {a^{p - 1} - 1} p$

## Also defined as

Some sources define and denote the Fermat quotient as:

$\map {\delta_p} a = \dfrac {a - a^p} p$

## Source of Name

This entry was named for Pierre de Fermat.