Vol. 7 (2023)
Articles

Ley de reciprocidad cuadrática y aplicaciones

Artículo (PDF) (Español (España))
  • Mario Pérez Maletzki

Published 08/07/2023

Keywords

  • Ley de reciprocidad cuadrática,
  • GAP,
  • residuo cuadrático,
  • símbolo de Legendre

How to Cite

Pérez Maletzki, Mario. «Ley de reciprocidad cuadrática y aplicaciones». En: TEMat, 7 (2023), págs. 51-66. ISSN: 2530-9633. URL: https://temat.es/articulo/2023-p51.

Copyright (c) 2023 Mario Pérez Maletzki

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

The goal of this survey is to introduce all the necessary concepts and theorems to provide a rigorous and self-contained proof of the Quadratic Reciprocity Law and see how this is a useful tool to obtain results such as the problem of the two squares, the problem of determining when a second degree congruence equation has any solution, to prove some properties about prime numbers and even to obtain information about the zero set of an elliptic curve.

We include examples specifically chosen to improve the understanding of those theorems. These examples have been created with the program GAP due to its convenience for this topic of mathematics and we include the codes so the reader can readily test them.

Artículo (PDF) (Español (España))