Ahmet Tekcan and Arzu Özkoç and Hatice Alkan
The Diophantine Equation y2 − 2yx − 3 0 and Corresponding Curves over Fp
925 - 928
2009
3
11
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/6133
https://publications.waset.org/vol/35
World Academy of Science, Engineering and Technology
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 ycoordinates of all rational points (x, y) on
Ep over Fp.
Open Science Index 35, 2009