Tópicos de funções aritméticas e o teorema de Euler

Abstract

This paper aims to present a short introduction to the study of Functions Arithmetic, presenting some properties giving a little more emphasis to the functions specific arithmetic, such as the Euler Function and the Möbius Function. We also highlight the Euler's theorem and a corollary of it, known as Fermat's Little Theorem that will serve as a basis for solving some problems that are often charged in Mathematics Olympics around the world. The idea of ​​Primitive Roots will also be addressed in this paper in order to provide the high school teacher with a powerful tool that is not taught in Basic Education. Finally, we dedicate a chapter only with problems on the subjects covered, presenting all the solutions of the themselves to support teachers.