Inter relationship between numbers congruent and elliptic curves

• Grant number: 16/17970-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: December 01, 2016
• End date: November 30, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Jaime Edmundo Apaza Rodriguez
• Grantee: Douglas Matheus Gavioli Dias
• Host Institution: Faculdade de Engenharia (FEIS). Universidade Estadual Paulista (UNESP). Campus de Ilha Solteira. Ilha Solteira , SP, Brazil

Abstract

This project's main objective study the interrelationship between a classic and old subject of Number Theory, Problem of Congruent Numbers and a recent one on the Arithmetic of Elliptic Curves. The Problem of Congruent Numbers is whether a natural number n can be realized as the area of a right triangle with rational sides. This problem is related to the existence rational points on some elliptic curve defined over the field of rational numbers Q. We will study this problem and its many variants. (AU)