O Décimo problema de Hilbert

• Ano de defesa: 2010
• Autor(a) principal: Ferreira, Marcelo
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Uberlândia; BR; Programa de Pós-graduação em Matemática; Ciências Exatas e da Terra; UFU
• Palavras-chave em Português: 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
• Link de acesso: https://repositorio.ufu.br/handle/123456789/16784

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.