A aritmética nas olimpíadas de matemática universitária

Abstract

Since ancient times, Mathematics has always been challenging, and many people solve mathematical problems for pleasure and fun. With the advent of the mathematical olympiads, these challenges turned into great competitions that spread throughout the world, being improved over time, and that pleasure and interest for the olympiads makes it possible that new competitions continue to emerge until the present day. This work presents a general approach of the national and international Mathematical Olympiads, specially the academical ones, because this modality is still little publicized and there are not many materials available about them. We started the work speaking about the main international olympiads, such as IMO, IMC, CIIM, OIMU, among others, presenting the best results of brazilians in each of them. In addition, we also address the national competitions and the few regional ones that have an academical level. We have also highlighted the female participation in the mathematics olympiads, showing the best results achieved by the brazilian women and the existing competitions aimed exclusively at the female audience. Next, we have some concepts related to Arithmetic, such as principle of induction, divisibility and congruences. After that, this work is finished with arithmetic questions selected from some academical level olympiads, with their appropriate solutions, thus creating a support material for those who desire to know more about the mathematical olympiads and see how some studied contents in basic and university education can be used in solving questions from these competitions.