Mémoire de Maîtrise
DOI
https://doi.org/10.11606/D.55.2020.tde-22012021-113841
Document
Auteur
Nom complet
Ana Catarina Bruxelas
Unité de l'USP
Domain de Connaissance
Date de Soutenance
Editeur
São Carlos, 2020
Directeur
Jury
Picon, Tiago Henrique (Président)
Dias, Ires
Ribeiro, Beatriz Casulari da Motta
Souza, Tatiana Miguel Rodrigues de
Titre en portugais
Aritmética modular e aplicações: criptografia RSA e calendário perpétuo
Mots-clés en portugais
Aritmética modular
Calendário perpétuo
Criptografia RSA
Resumé en portugais
Titre en anglais
Modular arithmetic and applications: RSA cryptography and perpetual calendar
Mots-clés en anglais
Divisibility
Modular arithmetic
Perpetual calendar
RSA Cryptography
Resumé en anglais
Topics in Modular Arithmetic are rarely worked in Basic Education and few teachers have proper training on the subject. In this dissertation, we sought to portray conceptual premises that collaborate with the teacher training and its practice in some topics on Modular Arithmetic. It was proposed to previously treat initial concepts around the idea of divisibility and, sequentially, to introduce the concept of congruence in a natural way. It sought to provide a deeper understanding of the theme and clarity in the theoretical understanding, supporting the presentation of the results and theorems related through applications and achievements of diverse and non-trivial examples. In this sense, relevant results from the study of congruences were shown, such as Fermats Theorem, Eulers Theorem, and equivalence classes. The RSA Cryptography system and the Perpetual Calendar were presented to illustrate some applications of the treated results. In conclusion, a didactic sequence proposal was presented for the final years of Elementary School, showing some concepts and results of Modular Arithmetic present in the Mathematics curriculum of this teaching stage and according to the Common National Curricular Base. To support the didactic sequence, it was used the analysis of the arithmetic and algebraic quantities and constructions possible in the current calendar, adopting as a guideline the conclusions made about the Perpetual Calendar and, consequently, about the Zeller Theorem.

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Date de Publication
2021-01-22

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