Bases numéricas na olimpíada internacional de matemática

Abstract

In this article we discuss in detail three problems that were proposed for the International Mathematical Olympiad (IMO) and that in a creative way deal with numerical bases. The intention is that these problems be used to train students preparing for international olympics. The material can also be used by university teachers and students. The first problem explores the ternary base in relation to arithmetic triples (three consecutive numbers in arithmetic progression). In the second problem it is asked to determine an element of a sequence that serves as a mixed base and can be correlated with the octal base. And in the third problem one must find the order of an element of a sequence that is used as prime code on a binary basis.