Números inteiros como soma de quadrados

Abstract

This paper is a survey on representation of integers as sums of squares for the cases where we have the sum of two, three and four squares. The idea is to study conditions so that we can ensure the representation of numbers that are written as the sum of two and four square. The central focus is the statement of the theorem of Lagrange four squares, although we have gone a little further studying Fermat' s technique of in nite descense and the case n = 3 of Fermat's last theorem. Finally, we work with the development of a didactic sequence that can be used in the nal grades of elementary school and middle school, addressing Chapter 2 of this dissertation.