Congruências e os critérios de divisibilidade

Abstract

The theme of this scientific work is "Congruencies" and its delimitation is "Congruencies and the criteria of divisibility", considering the following problem: when a whole number is divisible by 2 to 11, supported by the properties of Congruencies? Given this, the general objective is to use the Congruencies to prove the Divisibility Criteria by 2,3,4,5,6,7,8,9,10 and 11 and some guiding questions are shown. For this purpose, it was necessary to study the concepts of Congruences, Divisibility and the Divisibility Criteria. Consequently, the elaboration and application of the project obtained favourable results since it was possible to demonstrate all the divisibility rules proposed using Congruencies. This is a work of great relevance, both for the teacher and for students of Basic or Higher Education. The work is theoretically grounded by Filho (1981); Machado (2018); Santos (1998); Rosen (2011); Durbin (2008); Mcdowell (2022); Domingues and Iezzi (2003); Silva (2015), Rodrigues (2013) and Moura (2015). In chapter 1, some basic properties of Divisibility will be presented and demonstrated. In chapter 2, the congruence modulo 𝑚 will be defined and some of its properties will be demonstrated. In the last chapter, the Divisibility Criteria and the proof of these using congruences will be addressed. Keywords: congruencies. divisibility. criteria. properties