%0 Journal Article
	%A Musa Demirci and  Nazlı Yıldız İkikardeş and  Gökhan Soydan and  İsmail Naci Cangül
	%D 2007
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 1, 2007
	%T The Number of Rational Points on Elliptic Curves y2 = x3 + a3 on Finite Fields
	%U https://publications.waset.org/pdf/6891
	%V 1
	%X 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.
	%P 130 - 132