Definition:Primitive Root (Number Theory)

Definition
Let $a, n \in \Z_{>0}$, that is, let $a$ and $n$ be strictly positive integers.

Let the multiplicative order of $a$ modulo $n$ be $\map \phi n$, where $\map \phi n$ is the Euler phi function of $n$.

Then $a$ is a primitive root of $n$ or a primitive root modulo $n$.