{"title":"The Diophantine Equation y2 \u2212 2yx \u2212 3 = 0 and Corresponding Curves over Fp","authors":"Ahmet Tekcan, Arzu \u00d6zko\u00e7, Hatice Alkan","country":null,"institution":"","volume":35,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":925,"pagesEnd":929,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/6133","abstract":"In this work, we consider the number of integer solutions\r\nof Diophantine equation D : y2 - 2yx - 3 = 0 over Z and\r\nalso over finite fields Fp for primes p \u2265 5. Later we determine the\r\nnumber of rational points on curves Ep : y2 = Pp(x) = yp\r\n1 + yp\r\n2\r\nover Fp, where y1 and y2 are the roots of D. Also we give a formula\r\nfor the sum of x- and y-coordinates of all rational points (x, y) on\r\nEp over Fp.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 35, 2009"}