What Do Beginner Students From a Brazilian Licentiate Degree in Science Course Reveal Facing a Thematized Problem in Linear Diophantine Equations Context?

We consider fundamental to encourage and valorize themes belonging to the conjunction of Elementary Theory of Numbers and Algebra in the basic education, areas that present interesting and simple understanding contexts which allow developing problem solving strategies. This paper aimed to present the results of the application and analysis of a problem thematized in the linear Diophantine equations to beginner students from a Brazilian Licentiate degree in Science course. The methodology employed was based on the four phases of Didactic Engineering - preliminary analyzes, conception and priori analysis, experimentation and posteriori analysis - described in Artigue (1996; 2014; 2020). From the results, it was observed that all the students mobilized the trial-and-error as an initial tool to seek the entire solutions, by using arithmetic calculations. There were no manifestations of using algebraic writing as a basic support for solving the proposed problem, which represented an indication of the lack to understand the role of algebraic writing as a tool and potentiating strategy of mathematical problem solving.