# Solutions to Elementary Methods for Solving Diophantine Equations

Chapter

## Abstract

1. Solve the following equation in integers x, y :
$$x^{2} + 6xy + 8y^{2} + 3x + 6y = 2.$$
Solution. Write the equation in the form
$$(x + 2y)(x + 4y) + 3(x + 2y) = 2\quad{\rm or}\quad(x +2y)(x +4y + 3) = 2.$$
We obtain the solutions (0,−1), (3,−2), (3,−1), (6,−2).

## Keywords

Positive Integer Prime Divisor Integral Solution Integer Solution Diophantine Equation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Authors and Affiliations

• Titu Andreescu
• 1
Email author
• Dorin Andrica
• 2
• 3
• Ion Cucurezeanu
• 4
1. 1.School of Natural Sciences and MathematicsUniversity of Texas at DallasRichardsonUSA
2. 2.Faculty of Mathematics and Computer ScienceBabeş-Bolyai UniversityCluj-NapocaRomania
3. 3.Department of Mathematics College of ScienceKing Saud UniversityRiyadhSaudi Arabia
4. 4.Faculty of Mathematics and Computer ScienceOvidius University of ConstantaConstantaRomania