Linear Diophantine Equations: historical aspects and contributions in teaching and learning processes

Abstract

In studies of algebraic equations, it is common for students to have difficulties in understanding the concept studied, as well as its historical aspects. In the field of Number Theory, the study of Linear Diophantine Equations emerges, that are present in the trajectory of Mathematics teachers,

both in teaching and in the classroom, emphasizing the importance of Algebraic Education in Basic Education. Like this, the present study aims to discuss historical aspects of the Linear Diophantine Equations within the scope of the main mathematicians who contributed to the development of the concept, as well as understanding how this concept is evidenced in Brazilian scientific articles in educational processes. The Linear Diophantine Equations of two variables,  and , are of the form , with a, b and c integers, whose solutions are also integers.  For the development of this work, qualitative bibliographical research was used; the survey of studies took place on the Capes Periodicals Portal, in which the term “Linear Diophantine Equations” was inserted, as a descriptor. 15 scientific articles were mapped. It was concluded that the research indicates the thematic units: problem situations in Basic Education and Higher Education, Initial and Continuing Training of Teachers and application of the method to the Financial Market. Furthermore, the importance of Mathematics teachers is highlighted, to know and understand the history of Linear Diophantine Equations, to understand the difficulties faced by mathematicians themselves in developing the concept, which had at its core the social context, economic and cultural of each era.