@article{(Open Science Index):https://publications.waset.org/pdf/726, title = {The Number of Rational Points on Conics Cp,k : x2 − ky2 = 1 over Finite Fields Fp}, author = {Ahmet Tekcan}, country = {}, institution = {}, abstract = {Let p be a prime number, Fp be a finite field, and let k ∈ F*p. In this paper, we consider the number of rational points onconics Cp,k: x2 − ky2 = 1 over Fp. We proved that the order of Cp,k over Fp is p-1 if k is a quadratic residue mod p and is p + 1 if k is not a quadratic residue mod p. Later we derive some resultsconcerning the sums ΣC[x]p,k(Fp) and ΣC[y]p,k(Fp), the sum of x- and y-coordinates of all points (x, y) on Cp,k, respectively. }, journal = {International Journal of Mathematical and Computational Sciences}, volume = {1}, number = {1}, year = {2007}, pages = {75 - 78}, ee = {https://publications.waset.org/pdf/726}, url = {https://publications.waset.org/vol/1}, bibsource = {https://publications.waset.org/}, issn = {eISSN: 1307-6892}, publisher = {World Academy of Science, Engineering and Technology}, index = {Open Science Index 1, 2007}, }