TY - JFULL
AU - Ahmet Tekcan and Arzu Özkoç and Hatice Alkan
PY - 2009/12/
TI - The Diophantine Equation y2 − 2yx − 3 = 0 and Corresponding Curves over Fp
T2 - International Journal of Mathematical and Computational Sciences
SP - 924
EP - 928
VL - 3
SN - 1307-6892
UR - https://publications.waset.org/pdf/6133
PU - World Academy of Science, Engineering and Technology
NX - Open Science Index 35, 2009
N2 - 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.
ER -