The Number of Rational Points on Conics Cp,k : x2 − ky2 = 1 over Finite Fields Fp
نویسنده
چکیده
Let p be a prime number, Fp be a finite field, and let k ∈ Fp. In this paper, we consider the number of rational points on conics Cp,k : x − ky = 1 over Fp. We proved that the order of Cp,k over Fp is p− 1 if k is a quadratic residue mod p and is p+1 if k is not a quadratic residue mod p. Later we derive some results concerning the sums ∑ C [x] p,k(Fp) and ∑ C [y] p,k(Fp), the sum of x− and y−coordinates of all points (x, y) on Cp,k, respectively. Keywords— elliptic curve, conic, rational points.
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