Geometria aritmética : triplas pitagóricas e números inteiros que são soma de dois quadrados

Abstract

This dissertation has as its theme the triples of natural numbers that can be the measures of the sides of a right triangle. These numbers are characterized at the beginning of the work, using Elementary Number Theory. Then several methods are developed using “Arithmetic Geometry”, such as Linear Diophantine Equations, Pick Theorem, Fermat Tangent and Secant Method, Projective Curves, Reticulated, Flat Torus, and Minkowski’s Theorem. Finally, using these geometric and arithmetical methods, the characterization of the integers that is the sum of two squares, which corresponds to the natural numbers that can be hypotenuse of a right triangle.