Uma introdução aos inteiros gaussianos

Abstract

This monograph presents the principles of number theory, formally establishing important arithmetic facts that characterize the systems in question. It sought to develop theory in an axiomatic way, from the principles of sets, which constitute the main tool for mathematical rigor. Furthermore, this text presents different domains of integrity, which have many similarities, although for each of these there are specific considerations and precautions to be taken. From this development of systems analogous to the set of whole numbers, it is possible to contemplate a series of interesting facts and structures, as well as to promote a good understanding of properties suitable to be worked on in more contexts. The text also deals with the set of Gaussian integers, which is still not so often worked on, but presents an interesting potential for studying integers.