{"title":"Group of p-th Roots of Unity Modulo n","authors":"Rochdi Omami, Mohamed Omami, Raouf Ouni","volume":43,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":979,"pagesEnd":991,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10881","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.<\/p>\r\n","references":"[1] R. Omami, M. Omami and R. Ouni, Group of Square Roots of Unity\r\nModulo n. International Journal of Computational and Mathematical\r\nSciences, 2009\r\n[2] J-P. Serre, A Course in Arithmetic. Graduate Texts in Mathematics,\r\nSpringer, 1996\r\n[3] S. Lang, Undergraduate Algebra, 2nd ed. UTM. Springer Verlag,1990\r\n[4] Hardy, G. H, Ramanujan: Twelve Lectures on Subjects Suggested by His\r\nLife and Work, 3rd ed. New York: Chelsea, 1999. G. H.\r\n[5] H. Cohen, A course in computational algebraic number theory.\r\nSpringer-Verlag, 1993.\r\n[6] V. Shoup, A Computational Introduction to Number Theory and Algebra.\r\nCambridge University Press, 2005.\r\n[7] David M. Bressoud, Factorization and Primality Testing. Undergraduate\r\nTexts in Mathematics, Springer-Verlag, New York, 1989.\r\n[8] Elwyn R. Berlekamp. Factoring Polynomials Over Finite Fields. Bell\r\nSystems Technical Journal, 46:1853-1859, 1967.\r\n[9] David G. Cantor and Hans Zassenhaus. A New Algorithm for Factoring\r\nPolynomials Over Finite Fields. Mathematics of Computation, 36:587-\r\n592, 1981.\r\n[10] Frank Garvan. The Maple Book. Chapman and Hall\/CRC, Boca Raton,\r\nFL 2002","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 43, 2010"}