Fermat’s little theorem states that if $p$ is a prime number, then for any integer $a$, the number $a^p - a$ is an integer multiple of $p$. In the notation of modular arithmetic, this is expressed as

$$
begin{align*}
a^p equiv a: (mod p)
end{align*}
$$

To be continued

Reference

• Fermat’s little theorem
• Proof of Fermat’s Little Theorem