Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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MULTIPLICATIVE GROUPS OF INTEGERS WITH SEMI-PRIMITIVE ROOTS MODULO n

  • Lee, Ki-Suk (Department of Mathematics Education Korea National University of Education) ;
  • Kwon, Miyeon (Department of Mathematics University of Wisconsin-Platteville) ;
  • Shin, GiCheol (Department of Mathematics Education Korea National University of Education)
  • Received : 2012.05.29
  • Published : 2013.01.31
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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.

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References

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