A positive integer $n$ has a primitive root modulo $n$ iff either $n\in\{1,2,4\}$ or
\begin{align*}
n=p^a \quad \text{or} \quad n=2p^a,
\end{align*}
where $p$ is an odd prime and $a\in\mathbb{N}$.
Knowledge Status
Algebra
Discussion
Classifies the positive moduli for which the multiplicative group of [units modulo n](/theorems/735) is cyclic and hence admits a primitive root.
Proof
No proof available for this theorem.
Prerequisites
(0/2 completed)
Prerequisites Graph
Interactive dependency map showing how this theorem builds on foundational concepts