Aspectos aritméticos da sequência de Fibonacci

Abstract

This research was elaborated with the objective of using arithmetic means to study and prove properties of the Fibonacci sequence, properties that were described along the time by mathematicians of the whole world. It will be given focus to the historical context so that it is possible to understand from where it appeared such presented sequence, and also to the arithmetic theory of the numbers, so that the suggested proposal could be effective. Not less important, we will also dedicate a section to the mathematician Édouard Lucas, who was responsible for the popularization of the Fibonacci sequence having today, as homage, his own sequence that, as we will see throughout this work, is directly related to the Fibonacci sequence. The main authors are Bruno A. e Silva, Edgard de A. Filho, Thomas Koshy, and Kenneth H. Rosen. Key-words: Number Theory. Fibonacci sequence. Lucas Sequence.