SEMI-PRIMITIVE ROOT MODULO n

• Lee, Ki-Suk (Department of Mathematics Education, Korea National University of Education) ;
• Kwon, Mi-Yeon (Department of Mathematics, University of Wisconsin-Platteville) ;
• Kang, Min-Kyung (Department of Mathematics Education, Korea National University of Education) ;
• Shin, Gi-Cheol (Department of Mathematics Education, Korea National University of Education)
• Accepted : 2011.03.25
• Published : 2011.06.25
• 101 23

Abstract

Consider a multiplicative group of integers modulo n, denoted by $\mathbb{Z}_n^*$. Any element $a{\in}\mathbb{Z}_n^*$ 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 classify the multiplicative groups of integers having semi-primitive roots and give interesting properties of such groups.

Keywords

Multiplicative group of integers modulo n;primitive roots;semi-primitive roots

References

1. M. Abramowitz, I. A. Stegunl, Handbook of Mathematical Functions, Dover Publication, New York, 1964.
2. C. F. Gauss; A. A. Clarke (translator into English), Disquisitiones Arithemeticae, Springer, New York, 1986.
3. H. Riesel, Prime Numbers and Computer Methods for Factorization, Birkhauser, Boston, 1994.
4. H. E. Rose, A Course in Number Theory, Oxford University Press Inc., New York, 1994
5. J. K. Strayer, Elementary Number Theory, Waveland Press, Inc., 2002.

Cited by

1. MULTIPLICATIVE GROUPS OF INTEGERS WITH SEMI-PRIMITIVE ROOTS MODULO n vol.28, pp.1, 2013, https://doi.org/10.4134/CKMS.2013.28.1.071