Tópicos de funções aritméticas e o teorema de Euler

• Ano de defesa: 2020
• Autor(a) principal: Carvalho, Lucas Moisés Carneiro de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Palavras-chave em Português: Funções Aritméticas; Função de Euler; Função de Möbius; Teorema de Euler; Pequeno Teorema de Fermat; Raízes Primitivas; Matematica - problemas e exercícios; Arithmetic functions; Euler function; Möbius function; Euler's theorem; Fermat’s little theorem; Primitive Roots.; Mathematics – problems and exercises
• Link de acesso: http://www.repositorio.ufc.br/handle/riufc/53470

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.