{"title":"Group of Square Roots of Unity Modulo n","authors":"Rochdi Omami, Mohamed Omami, Raouf Ouni","volume":31,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":505,"pagesEnd":514,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/8554","abstract":"Let n \u2265 3 be an integer and G2(n) be the subgroup\nof square roots of 1 in (Z\/nZ)*. In this paper, we give an algorithm\nthat computes a generating set of this subgroup.","references":"[1] J-P. Serre, A Course in Arithmetic. Graduate Texts in Mathematics,\nSpringer, 1996\n[2] S. Lang, Undergraduate Algebra, 2nd ed. UTM. Springer Verlag,1990\n[3] H. Cohen, A course in computational algebraic number theory.\nSpringer-Verlag, 1993.\n[4] V. Shoup, A Computational Introduction to Number Theory and Algebra.\nCambridge University Press, 2005.\n[5] David M. Bressoud, Factorization and Primality Testing. Undergraduate\nTexts in Mathematics, Springer-Verlag, New York, 1989.\n[6] E. Bach, A note on square roots in finite fields. IEEE Trans. Inform.\nTheory, 36(6):1494-1498, 1990. Eric\n[7] E. Bach and K. Huber, Note on taking square-roots modulo N. IEEE\nTransactions on Information Theory, 45(2):807809, 1999.\n[8] D. Shanks, Five number-theoretic algorithms. In Proc. Second\nMunitoba Conf. Numerical Math. 51-70, 1972.\n[9] Hardy, G. H, Ramanujan: Twelve Lectures on Subjects Suggested by His\nLife and Work, 3rd ed. New York: Chelsea, 1999. G. H.\n[10] Hardy and E. M.Wright, An introduction to the theory of numbers,\n4th ed. Oxford University Press, 1960.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 31, 2009"}