Divisibilidade, congruência e aritmética modular em problemas olímpicos.

Abstract

Mathematics is a living and constantly growing science, not only in the everyday life of individuals, but also in universities. In this sense, in order to disseminate mathematical knowledge in both Basic and Higher Education, the Mathematical Olympiads were created, a project at the international, national, regional and local levels, with the purpose of stimulating and promoting the study of Mathematics , thus contributing to a quality basic education. In the present work we approach a little about the origin of the Mathematical Olympiads, we discuss about the emergence and the objectives of the main olympiads, some international: International Mathematical Olympiad (IMO); Ibero-American Mathematics; South Cone and the Olympiad of May and national: Brazilian Olympiad of Mathematics of the Public Schools (OBMEP) and the Brazilian Mathematical Olympiad (OBM) and, regionally, we talked about the Olympiad Campinense de Matemática (OCM), Olympiad promoted and held by the University Federal University of Campina Grande (UFCG). In line with the problems addressed by these competitions, we have dealt with concepts related to Number Theory such as divisibility, congruences and modular arithmetic. This paper aims to justify the need to construct a support material that includes teachers and students from public and private schools interested in preparing for the Mathematical Olympiads. The intention is not to use this material as an olympics course, as it is far from complete, but can be used to review some important topics related to Number Theory.