MULTIPLICATIVE GROUPS OF INTEGERS WITH SEMI-PRIMITIVE ROOTS MODULO n

Title & Authors
MULTIPLICATIVE GROUPS OF INTEGERS WITH SEMI-PRIMITIVE ROOTS MODULO n
Lee, Ki-Suk; Kwon, Miyeon; Shin, GiCheol;

Abstract
Consider a multiplicative group of integers modulo $\small{n}$, denoted by $\small{\mathbb{Z}_n^*}$. Any element $\small{a{\in}\mathbb{Z}_n^*}$ is said to be a semi-primitive root if the order of $\small{a}$ modulo $\small{n}$ is $\small{{\phi}(n)/2}$, where $\small{{\phi}(n)}$ 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;
Language
English
Cited by
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