Interseção de números geométricos via equação de Pell
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Data
2015-07-06
Autores
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Universidade Federal de Goiás
Resumo
Our work had as main objective to study the intersection of integer sequences, denominated
polygonal numbers, through Pell's equation. In this context, the solution
of two equations will be treated: x2 Dy2 = 1 and x2 Dy2 = N, jNj > 1. For
the rst one we have used results from the theory of continued fractions. For the last
one, we have used the method of solution delineated in literature. Besides, propositions
referring to the intersection of polygonal numbers for some particular cases are
presented and demonstrated. Also, the proposition of the general case is presented and
demonstrated. Finally, we have performed the solution of some of Pell's equations in
order to determine the intersection of some polygonal numbers.
Descrição
Palavras-chave
Números geométricos, Frações contínuas, Equação de Pell, Interseção, Polygonal numbers, Continued fractions, Pell's equation, Intersection
Citação
SILVA, R. P. Interseção de números geométricos via equação de Pell. 2015. 98 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Universidade Federal de Goiás, Catalão, 2015.