Sistema de equações diofantinas não lineares

Abstract

This dissertation aims to present a method for solving equations nonlinear diophantine lines that has its origins in the work of (Mordell, 1952) whose title é: “The Congruence ax3 + by3 + c ≡ 0(modxy), and integer solutions of cubic equations in three variables”. This method was applied by several authors to solve equations quadratic and cubic. Specifically, we will present the application of the method in systems of non-linear diophantine equations based on the articles “A system of quadratic diophantine equation” (Mills, 1953) and “A system of cubic diophantine equation” (Mohanty, 1977). Heuristically, the method consists of producing a sequence of solutions from a initial solution. The sequences thus produced are called chains and satisfy certain requirements. rigidity conditions which allow inferences about the finiteness of its quantity. This information in turn allows us to draw conclusions about the nature of the solutions of the equations under study.