# Definition:Primitive Root

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 $\phi \left({n}\right)$, where $\phi \left({n}\right)$ is the Euler phi function of $n$.
Then $a$ is a primitive root of $n$ or a primitive root modulo $n$.