Definition:Primitive Root (Number Theory)

This page is about Primitive Root in the context of Number Theory. For other uses, see Primitive Root.

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 $n$.

Sources

• 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): $\S 3.4$: Cyclic groups