Detalhes bibliográficos
Ano de defesa: |
2019 |
Autor(a) principal: |
Oliveira, Francisco Erilson Freire de |
Orientador(a): |
Não Informado pela instituição |
Banca de defesa: |
Não Informado pela instituição |
Tipo de documento: |
Dissertação
|
Tipo de acesso: |
Acesso aberto |
Idioma: |
por |
Instituição de defesa: |
Não Informado pela instituição
|
Programa de Pós-Graduação: |
Não Informado pela instituição
|
Departamento: |
Não Informado pela instituição
|
País: |
Não Informado pela instituição
|
Palavras-chave em Português: |
|
Link de acesso: |
http://www.repositorio.ufc.br/handle/riufc/44231
|
Resumo: |
The purpose of this dissertation is to present different demonstrations for one of the most important theorems in Number Theory, namely Fermat's Little Theorem. Our interest in this claim is to show the interrelationships between the most diverse areas of mathematics. Our work, in a sense, is also a bibliographical research. Initially, we make a brief survey about the history of Pierre de Fermat, listing some of his various contributions to mathematics, especially to the theory of numbers. We continue in the second chapter, presenting the best known demonstrations for Fermat's Little Theorem. In the third chapter, we begin the alternative demonstrations, first presenting one by Combinatorial Analysis, consequently using introductory ideas of Graph Theory and concluding with a demonstration that uses the Taylor Series as its main content. In the next chapter, we bring up a demonstration using the ideas of Dynamic Systems and then develop a demonstration via Group Theory. Finally, we present our considerations about the work developed, emphasizing Pierre de Fermat's contributions to Mathematics, the interrelationships between the most diverse areas of this Science and the importance of using mathematical demonstrations for students of Basic Education. |