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:
 * $q_p \left({a}\right) = \dfrac {a^{p - 1} - 1} p$

Also defined as
Some sources define and denote the Fermat quotient as:
 * $\delta_p \left({a}\right) = \dfrac {a - a^p} p$