Teoria dos Números: praticando a resolução de problemas Olímpicos

Abstract

Number theory is branch from Mathematics hardly ever explored in elementary and middle school, almost nonexistent in high school. Its implementations and features in elementary and middle school narrow in divisibility principals, greatest common factor (GCF) and Euclidean algorithm. All presented in a plain and timid way. Nevertheless, number theory is a vast field in Mathematics, tightly related to algebra results. It consists of powerful tools to the resolutions of problems such as: Olympics, properties display and indirect implementations in other sciences. In this paper, it will be presented in a fair and concise, the most fundamental outcome related to number theory which do not need further studies to be understood. One familiarity with the properties of integers, the aspects of divisibility seen in elementary and middle school and notions of mathematical proof are sufficient to the knowledge of the main idea of this paper. The major results presented were: Euclidean algorithm, fundamental theorem of arithmetic, Fermat, Wilson and Euler’s theorem and Euler’s totient function . During demos, it will be presented exercises that exemplifies theory. Besides, there are 2 chapters concerning the resolution of Olympics problems, with the intentions to explore, in a smart way, the concepts presented during theory.