CONTINUED FRACTIONS, DETERMINANTS AND LINEAR DIOPHANTINE EQUATIONS

Delfim Dias Bonfim, Gilmar Pires Novaes

Abstract


http://dx.doi.org/10.5902/2179460X14468

This article is intended to present a method for solving linear diophantine equations, using for this purpose, the concepts of continuous fractions and determinants. Initially we present the definition of simple continued fraction, geometric interpretation and some fundamental theorems related to this concept. Subsequently we relate the finite simple continued fractions with determinants. Finally we present the definition of linear Diophantine equation and we demonstrate the method to solve it using the concepts mentioned above.


Keywords


Frações contínuas, Determinantes, Equações diofantinas lineares.



DOI: http://dx.doi.org/10.5902/2179460X14468

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