Inteiros que se escrevem como soma de quatro quadrados

• Ano de defesa: 2015
• Autor(a) principal: Figueiredo, João Luis de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Mato Grosso; Brasil; Instituto de Ciências Exatas e da Terra (ICET); UFMT CUC - Cuiabá; Programa de Pós-Graduação em Matemática - PROFMAT
• Palavras-chave em Português: Soma de quadrados; Identidade de Lagrange; Teorema de lagrange; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA; Sum of squares; Lagrange identity; Theorem of lagrange
• Link de acesso: http://ri.ufmt.br/handle/1/2190

The problem of writing a number as a sum of squares, mainly prime numbers, is very old and may have emerged from the investigations of Fermat in the seventeenth century. Years later, the Fermat himself demonstrated using complex numbers, that every prime number of the form 4k+1 can be written as a sum of two squares. But through some cases, certain figures could not be represented in this format, continuing the idea of establishing some more conditions so that they could be written as the sum of three squares, until we reach the general appearance that any number can be represented as a sum of four squares (Theorem of Lagrange).