O Décimo problema de Hilbert
In this work we present a proof that the Hilbert s Tenth Problem is unsolvable. This problem is to give a computing algorithm which will tell of a given polynomial Diophantine equation with integer coefficients whether or not it has a solution in integers. We start developing some topics of basic nu...
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| Tipo de recurso: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2010 |
| País: | Brasil |
| Institución: | Universidade Federal de Uberlândia (UFU) |
| Repositorio: | Repositório Institucional da UFU |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufu.br:123456789/16784 |
| Acceso en línea: | https://repositorio.ufu.br/handle/123456789/16784 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometria algébrica Riemann-Hilbert, Problemas de Equações diofantinas Funções recursivas Função exponencial Diophantine Eeuations Recursive functions Exponential function CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| Sumario: | In this work we present a proof that the Hilbert s Tenth Problem is unsolvable. This problem is to give a computing algorithm which will tell of a given polynomial Diophantine equation with integer coefficients whether or not it has a solution in integers. We start developing some topics of basic number theory, that will be useful at some time. In this part we prove only main results. After that, we study Diophantine equation as well as Diophantine functions. Then, we prove a serie of lemas that will be useful to proof that the exponential function is Diophantine. From there, we define the concept of recursive function and prove that a function is Diophantine if and only if it is recursive. Finally we prove the Universality Theorem. We use this last theorem to proof that the Hilbert s Problem is unsolvable. |
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