Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30172
Group of p-th Roots of Unity Modulo n

Authors: Rochdi Omami, Mohamed Omami, Raouf Ouni

Abstract:

Let n ≥ 3 be an integer and p be a prime odd number. Let us consider Gp(n) the subgroup of (Z/nZ)* defined by : Gp(n) = {x ∈ (Z/nZ)* / xp = 1}. In this paper, we give an algorithm that computes a generating set of this subgroup.

Keywords: Group, p-th roots, modulo, unity.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1076098

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 710

References:


[1] R. Omami, M. Omami and R. Ouni, Group of Square Roots of Unity Modulo n. International Journal of Computational and Mathematical Sciences, 2009
[2] J-P. Serre, A Course in Arithmetic. Graduate Texts in Mathematics, Springer, 1996
[3] S. Lang, Undergraduate Algebra, 2nd ed. UTM. Springer Verlag,1990
[4] Hardy, G. H, Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, 1999. G. H.
[5] H. Cohen, A course in computational algebraic number theory. Springer-Verlag, 1993.
[6] V. Shoup, A Computational Introduction to Number Theory and Algebra. Cambridge University Press, 2005.
[7] David M. Bressoud, Factorization and Primality Testing. Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1989.
[8] Elwyn R. Berlekamp. Factoring Polynomials Over Finite Fields. Bell Systems Technical Journal, 46:1853-1859, 1967.
[9] David G. Cantor and Hans Zassenhaus. A New Algorithm for Factoring Polynomials Over Finite Fields. Mathematics of Computation, 36:587- 592, 1981.
[10] Frank Garvan. The Maple Book. Chapman and Hall/CRC, Boca Raton, FL 2002