Multiplicative groups of integers with semi-primitive roots modulo $n$
Commun. Korean Math. Soc. 2013 Vol. 28, No. 1, 71-77
https://doi.org/10.4134/CKMS.2013.28.1.71
Printed January 31, 2013
Ki-Suk Lee, Miyeon Kwon, and GiCheol Shin
Korea National University of Education, University of Wisconsin-Platteville, Korea National University of Education
Abstract : 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
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