@article{(Open Science Index):https://publications.waset.org/pdf/6891, title = {The Number of Rational Points on Elliptic Curves y2 = x3 + a3 on Finite Fields}, author = {Musa Demirci and Nazlı Yıldız İkikardeş and Gökhan Soydan and İsmail Naci Cangül}, country = {}, institution = {}, abstract = {In this work, we consider the rational points on elliptic curves over finite fields Fp. We give results concerning the number of points Np,a on the elliptic curve y2 ≡ x3 +a3(mod p) according to whether a and x are quadratic residues or non-residues. We use two lemmas to prove the main results first of which gives the list of primes for which -1 is a quadratic residue, and the second is a result from [1]. We get the results in the case where p is a prime congruent to 5 modulo 6, while when p is a prime congruent to 1 modulo 6, there seems to be no regularity for Np,a.}, journal = {International Journal of Mathematical and Computational Sciences}, volume = {1}, number = {1}, year = {2007}, pages = {130 - 132}, ee = {https://publications.waset.org/pdf/6891}, 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}, }