Aplicações combinatórias à teoria dos números

Abstract

The Number theory and Combinatorics are two important branches of mathematics that have some of their basic concepts addressed in elementary and high school. In Brazil, these areas of mathematics are the subject covered in several assessment exams, such as the Brazilian Mathematical Olympiad of Public Education, and the Brazilian National High School Exam. The Number theory studies the integers and their properties, while Combinatorics studies the occurrence of certain events and determines how many of them exist, when possible. This work applies combinatorial concepts in the derivation of several results from the Number theory. In this study presented several combinatorial principles, such as the bijection principle, the addition principle, the multiplication principle, the inclusion–exclusion principle, and the pigeonhole principle. At least, they are presented proofs of the Fermat’s little theorem and the Wilson’s theorem using combinatorial principles. This work seeks to arouse students’ interest to the importance of these subjects, thus facilitating and paving the way to teaching-learning process.