# Giuga number

## Definition

A composite number  is termed a Giuga number if and only if it satisfies the following equivalent conditions:

1. For every prime number  dividing , we have that  divides , or equivalently, that  divides .
2. We have the following congruence:



where  denotes the Euler totient function of .

Note that all prime numbers satisfy the stated condition but we deliberately exclude them by imposing the restriction of being composite.