Inteiros que são somas de dois quadrados:

Abstract

This work brings with it a study on Number Theory. Its main objective is to prove Fermat's perfect square theorem, that is, to establish which whole numbers can be written as the sum of two perfect squares x^2 + y^2, x, y ∈ Z and as a secondary objective to demonstrate which ones cannot be written in such a way. Along with these demonstrations, we have as a complement the history and curiosities about the theorems and the contents contained in this research. The work is qualitative bibliographical research, where we base ourselves on studies already pre- established: books and scientific articles. During this work, the definitions and results of several contents that corroborate the main demonstration were established. As a result, the numbers that can and cannot be formed by the sum of two squares were presented in a generalized way. Thus, a clearer view of the theorem and its demonstration can be concluded from the bibliographical works.