Journal article
The circle equation over finite fields
Department of Electrical Engineering, Technical University of Denmark1
Center for Electric Power and Energy, Centers, Technical University of Denmark2
Distributed Energy Resources, Center for Electric Power and Energy, Centers, Technical University of Denmark3
Department of Applied Mathematics and Computer Science, Technical University of Denmark4
Cognitive Systems, Department of Applied Mathematics and Computer Science, Technical University of Denmark5
Interesting patterns in the geometry of a plane algebraic curve C can be observed when the defining polynomial equation is solved over the family of finite fields. In this paper, we examine the case of C the classical unit circle defined by the circle equation x2 + y2 = 1. As a main result, we establish a concise formula for the number of solutions to the circle equation over an arbitrary finite field.
We also provide criteria for the existence of diagonal solutions to the circle equation. Finally, we give a precise description of how the number of solutions to the circle equation over a prime field grows as a function of the prime.
Language: | English |
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Publisher: | Taylor & Francis |
Year: | 2018 |
Pages: | 665-674 |
ISSN: | 1727933x and 16073606 |
Types: | Journal article |
DOI: | 10.2989/16073606.2017.1395774 |
ORCIDs: | Aabrandt, Andreas |