Fermat's Little Theorem

number-theory

Definition

Fermat's Little Theorem

Fermat’s little theorem is a special case of Euler’s theorem: For any prime $p$ and any integer $a$ not divisible by $p$:

$$a^{p-1}\equiv 1(\mathrm{mod}p)$$

Equivalently, for any integer $a$:

$$a^p\equiv a(\mathrm{mod}p)$$