2014-09-232013-03-01BORGES, Fábio Vieira de Andrade. Equações diofantinas lineares em duas incógnitas e suas aplicações. 2013. 63 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Universidade Federal de Goiás. Goiânia, 2013.http://repositorio.bc.ufg.br/tede/handle/tede/3124The main objective of this assignment is to help students and also teachers with the resolution and understanding of problems involving the Linear Diophantine Equations with Two Incognits through the elaboration and application of didactic activities in order to contribute to the study of this kind of equations. Through the tasks it was aimed to dothe integration of Arithmetic with Algebra and Geometry by using some computational programs which worked as support to the graphical visualization of the entire solutions. In the first chapters the essence of the Elementary Theory of Numbers will be better known, since the mathematical tools which will be used to solve linear Diophantine equations will be displayed and demonstrated, some of them already known, like the greatest common divisor (g.d.c). Then the Diophantine equations and theirapplication methods for the solution of daily problems will be introduced. The Conclusion of this study highlights the importance of algebraic and geometric interpretation of Linear Diophantine Equations, and also emphasizes that the contact with problems of this area contributes to the students reasoning abilities development in a creative way. It is important to emphasize that this issue can be introduced in high school.application/pdfAcesso AbertoTeoria elementar dos númerosEquações diofantinas linearesEnsino médioSoluções inteirasResolução de problemasElementary theory of numbers,Linear diophantine equationsHigh schoolEntire solutionsProblem resolutionMATEMATICA::MATEMATICA APLICADADissertação