METHOD FOR SOLVING DIOPHANTINE EQUATIONS WITH COEFFICIENTS IN THE SET OF RATIONAL NUMBERS

Josias Neubert Savóis, Daiane Freitas

Abstract


http://dx.doi.org/10.5902/2179460X14529

Develop a solid understanding of linear Diophantine equations in two variables facilitates the resolution of many problems of daily life and also the real understanding of some mathematical concepts taught in school but they seem useless and without practical application. Moreover, the relationships that these equations are established with other content that are already inserted into the basic education justify their education and become an important tool for contextualizing and interdisciplinarity. This work also aims to show the importance of teaching of rational numbers and in this context do analysis on a new concept of greatest common divisor,called generalized maximum common divisor, and thus we can use the numberpad as rational coefficients of Diophantine equations, expanding the breadth of problems solved by these equations. The creation of various practical problems of implementation of the theory studied serves to convince us of the importance of this work and to encourage their implementation and creating new problems taking into account the reality of each school and its students.


Keywords


Equações diofantinas; números racionais; problemas práticos; conteúdos relacionados.



DOI: http://dx.doi.org/10.5902/2179460X14529

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