The Number of Rational Points on Elliptic Curves and Circles over Finite Fields

In elliptic curve theory, number of rational points on elliptic curves and determination of these points is a fairly important problem. Let p be a prime and Fp be a finite field and k ∈ Fp. It is well known that which points the curve y2 = x3 + kx has and the number of rational points of on Fp. Consider the circle family x2 + y2 = r2. It can be interesting to determine common points of these two curve families and to find the number of these common points. In this work we study this problem.

Authors:

• Betül Gezer
• Ahmet Tekcan
• Osman Bizim

Keywords:

• Elliptic curves over finite fields
• rational points on elliptic curves and circles.

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