O método de circulantes, as fórmulas de Cardano e o teorema de Fermat para n=3

• Ano de defesa: 2017
• Autor(a) principal: Melo, Rômulo de Oliveira Lins Vieira de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Matemática; Programa de Pós-Graduação em Matemática; UFPB
• Palavras-chave em Português: Matrizes Circulantes; Equações Polinomiais; Fórmulas de Cardano; Teorema de Fermat; Circulating Matrices; Polynomial Equations; Cardano Formulas; Fermat Theorem; CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/9835

In this present work, principles and theorems associated to integers are returned, as well as eigenvalues and eigenvectors problems, highlighting a Hermitian matrix. Then it is emphasized to the Circulating Matrices, through which it is found the association to two well-defined polynomials: the representative and the characteristic. Later a brief account about the history of polynomial equations is made, drafting the Cardano-Tartaglia Formulas associated to them. Afterwards a unification is made in the resolution process of the polynomial equations of smaller degrees than the equal to 4, by means of the circulating matrices. The work is completed by proving a Fermat theorem for n = 3, using the Cardano-Tartaglia Formulas.