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1. Matos, Jair da Silva. Aritm?tica e aplica??es.

Degree: 2017, Universidade Federal do Amazonas

Essa disserta??o de conclus?o de curso tem por objetivo apresentar sucintamente algumas aplica??es imediatas, embora n?o-triviais de Teoria dos N?meros-Aritm?tica, dentre as quais podemos destacar o Algoritmo de Euclides, congru?ncias modulares e o Teorema Chin?s dos Restos. Al?m destes t?picos abordados, damos uma aten??o especial no in?cio deste trabalho de conclus?o de curso a alguns dos grandes matem?ticos que contribu?ram ? aritm?tica entre eles, Diofante de Alexandria, Pierre de Fermat, Euclides de Alexandria entre outros. A estrutura da disserta??o ? a seguinte: No cap?tulo 2 tratamos da revis?o te?rica sobre os n?meros inteiros e suas propriedades. Destacamos o Princ?pio da Boa Ordena??o, que caracteriza os n?meros inteiros, tratamos de algumas proposi??es importantes, m?ximo divisor comum e suas propriedades, n?meros primos, o Teorema Fundamental da Aritm?tica, o Pequeno Teorema de Fermat, n?meros de Fermat, n?meros de Mersenne, n?meros Perfeitos e finalizamos o cap?tulo 2 com o estudo das congru?ncias e a aritm?tica dos restos. No cap?tulo 3 apresentamos algumas aplica??es e iniciamos com as Equa??es Diofantinas Lineares, Congru?ncias Lineares e suas resolu??es, o Teorema Chin?s dos Restos, Classes Residuais e, finalmente, resolvemos problemas que fizeram parte dos Exames Nacionais de Qualifica??o do PROFMAT desde 2012 at? 2017. Tais problemas s?o resolvidos com as ferramentas propostas no texto, lemas, teoremas, proposi??es e propriedades, que facilitam a resolu??o. Acreditamos que tais conte?dos servem para contribuir na forma??o do futuro professor do Ensino B?sico, assim como aprofundar os conhecimentos daqueles que j? labutam na ?rea do Ensino de Matem?tica.

This dissertation aims to present succinctly some immediate, thout not trivial, Number Theory- Arithmetic applications, among which we can highlight the Euclidean Algorithm, Modular Congruences and the Chinese Remainder Theorem. In addition to these topics, we give special attention at the great mathematicians who contributed to the arithmetic among them, Diophantus od Alexandria, Pierre de Fermat, Euclides of Alexandria among others. The structure of the dissertation is as follows: in chapter 2 we deal with the theoretical revision of integers and their properties. We emphasize the Well Ordering Principle, wich characterizes whole number, we deal with some important propositions, common maximum divisor and it?s properties, prime numbers, the Fundamental Theorem of Arithmetic, Fermat?s Little Theorem, Fermat numbers, Mersenne?s Numbers, Numbers Perfect, and we end with the study of Congruences and the Arithmetic of the Remains. In chapter 3 we present some applications that we started with the Linear Diophantine Equations, Linear Congruences and Their resolutions, the Chinese Residue Theorem, Residual Classes, and finaly we solve problems that were part of the PROFMAT National Qualification Exams from 2012 to 2017. Such proplems are solved with the tools proposed in the text, lemmas, theorems, propositions and…

Advisors/Committee Members: Oliveira, Nilomar Vieira de, 32311230204, http://lattes.cnpq.br/4870990824639847, Prata, Roberto Antonio Cordeiro, Amorim Neto, Alcides de Castro, [email protected].

Subjects/Keywords: Aritm?tica; Exame de Qualifica??o; Hist?ria da Aritm?tica; CI?NCIAS EXATAS E DA TERRA: MATEM?TICA

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APA (6th Edition):

Matos, J. d. S. (2017). Aritm?tica e aplica??es. (Masters Thesis). Universidade Federal do Amazonas. Retrieved from http://tede.ufam.edu.br/handle/tede/6123

Chicago Manual of Style (16th Edition):

Matos, Jair da Silva. “Aritm?tica e aplica??es.” 2017. Masters Thesis, Universidade Federal do Amazonas. Accessed August 13, 2020. http://tede.ufam.edu.br/handle/tede/6123.

MLA Handbook (7th Edition):

Matos, Jair da Silva. “Aritm?tica e aplica??es.” 2017. Web. 13 Aug 2020.

Vancouver:

Matos JdS. Aritm?tica e aplica??es. [Internet] [Masters thesis]. Universidade Federal do Amazonas; 2017. [cited 2020 Aug 13]. Available from: http://tede.ufam.edu.br/handle/tede/6123.

Council of Science Editors:

Matos JdS. Aritm?tica e aplica??es. [Masters Thesis]. Universidade Federal do Amazonas; 2017. Available from: http://tede.ufam.edu.br/handle/tede/6123

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