Communications of the
Korean Mathematical Society CKMS

Consider a multiplicative group of integers modulo $n$, denoted by $\mathbb{Z}_n^*$. Any element $a \in \mathbb{Z}_n^*$ is said to be a semi-primitive root if the order of $a$ modulo $n$ is $\phi(n)/2$, where $\phi (n)$ is the Euler phi-function. In this paper, we discuss some interesting properties of the multiplicative groups of integers possessing semi-primitive roots and give its applications to solving certain congruences.

Keywords: multiplicative groups of integers, primitive roots, semi-primitive roots

MSC numbers: 11A07