little ferrmats theorm

it states that if p is a prime number, then for any integer a, a p − a will be evenly divisible by p.

This can be expressed in the notation of modular arithmetic as follows:

A variant of this theorem is stated in the following form: if p is a prime and a is an integer coprime to p, then a p−1 − 1 will be evenly divisible by p. In the notation of modular arithmetic: