The Diophantine Equation y 2 − 2 yx − 3 = 0 and Corresponding Curves over F p
نویسندگان
چکیده
In this work, we consider the number of integer solutions of Diophantine equation D : y − 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 : y = Pp(x) = y p 1 + y p 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. Keywords—Diophantine equation, Pell equation, quadratic form.
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