primitive root
Given any positive integer , the group of units of the ring is a cyclic group iff is 4, or for any odd positive prime and any non-negative integer . A primitive root
is a generator
of this group of units when it is cyclic.
Equivalently, one can define the integer to be a primitive root modulo , if the numbers form a reduced residue system modulo .
For example, 2 is a primitive root modulo 5, sinceare all with 5 coprime positive integers less than 5.
The generalized Riemann hypothesis implies that every prime number
has a primitive root below .
References
Wikipedia, “Primitive root modulo n”