{"title":"The Number of Rational Points on Elliptic Curves and Circles over Finite Fields","authors":"Bet\u00fcl Gezer, Ahmet Tekcan, Osman Bizim","country":null,"institution":"","volume":19,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":477,"pagesEnd":483,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/12784","abstract":"In elliptic curve theory, number of rational points on\nelliptic curves and determination of these points is a fairly important\nproblem. Let p be a prime and Fp be a finite field and k \u2208 Fp. It\nis well known that which points the curve y2 = x3 + kx has and\nthe number of rational points of on Fp. Consider the circle family\nx2 + y2 = r2. It can be interesting to determine common points of\nthese two curve families and to find the number of these common\npoints. In this work we study this problem.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 19, 2008"}