THE PROBLEM OF FLAVIUS JOSEPHUS

Abstract

In this work we present a solution to the problem proposed by the mathematician Flavius ​​Josephus, in the first century after Christ. According to legend, a group of rebels, among them Josephus, were trapped in a cave by the enemy army. Preferring suicide to capture, the rebels decided to form a circle and the first one should kill the soldier directly to his side, thus until only one remains. The only solution would be to do the math and figure out the position of the soldier who would survive. The solution can be obtained solving the problem step by step, but if the number of soldiers is very large then the count becomes impracticable. To find such a solution with an arbitrary number of soldiers, we began our study with some concepts of potentiation, recurrence, and finite induction. Next, we introduce some concepts of binary numbers and their operations. This article is part of the research elaborated in the PET Mathematics group of the Federal University of Mato Grosso do Sul at Três Lagoas Campus.