# Matematica

Disponível somente no TrabalhosFeitos
• Páginas : 13 (3018 palavras )
• Publicado : 15 de junho de 2012

Amostra do texto
Anais do IX Seminário Nacional de História da Matemática
Sociedade Brasileira de História da Matemática

O Primeiro Trabalho de Euler sobre Equações Diofantinas
Euler’s First Work on Diophantine Equations
Joice de Andrade Dantas1 John A. Fossa2

Resumo

Abstract
Influenced by hisfriends, especially the Bernoullis and Goldberg, Leonhard Euler developed a strong intrest in the Theory of Numbers, including the resolution of Diophantine equations, that is, the resolution of equations whose coefficients and whose solutions are whole numbers. The first of Euler’s articles on this subarea of Number Theory was De solutione problematum diophanteorum per números integros (“On theSolution of Diophantine Problems in Whole Numbers”). It was only published in 1738, although it had been presented to the St. Petersburg Academy five years earlier. The problem that he addressed in the article is that of making the general second degree expression a perfect square. That is, he wants to find the whole number solutions to the equation ax2+bx+c = y2. In order to do so, Euler innovated byapplying algebraic methods to number theoretic problems and thereby showed how to generate new solutions from those already obtained. In his resolution, he reduced the original problem to the resolution of an associated equation, the so-called Pell equation, q2 = ap2+1. The reduction resolves the original problem since the solution to the Pell equation was already known. In fact, it was Eulerhimself who coined the term “Pell equation” since he apparently thought, erroneously, that it had been the English mathematician John Pell who had given the general solution to the aforementioned equation. In any case, Euler’s solution was inelegant in the sense that it required ever more
1 2

Mestranda do PPGEd da UFRN. E-mail: joy.dantas@gmail.com Depto. de Matemática, PPGEd e PPGECNM da UFRN....