Excellence in Research and Innovation for Humanity
%0 Journal Article
%A Ahmet Tekcan and  Arzu Özkoç and  Hatice Alkan
%D 2009 
%J  International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering
%B World Academy of Science, Engineering and Technology
%I International Science Index 35, 2009
%T The Diophantine Equation y2 − 2yx − 3 = 0 and Corresponding Curves over Fp
%U http://waset.org/publications/6133
%V 35
%X In this work, we consider the number of integer solutions
of Diophantine equation D : y2 - 2yx - 3 = 0 over Z and
also over finite fields Fp for primes p ≥ 5. Later we determine the
number of rational points on curves Ep : y2 = Pp(x) = yp
1 + yp
2
over Fp, where y1 and y2 are the roots of D. Also we give a formula
for the sum of x- and y-coordinates of all rational points (x, y) on
Ep over Fp.
%P 925 - 928