Diophantine Equations

In this book we present several types of Diophantine equations from simple to more complex. The aim of this work is to interest readers at different levels of knowledge and education. Therefore, this book is suitable for gifted high school students and university students. The text also contains word problems, which are tempting for readers who enjoy such problems. The book consists of eight chapters. In the first chapter, the authors present the Euclidean algorithm, an extended Euclidean algorithm for linear Diophantine equations with two unknowns. The second chapter deals with Diophantine linear equations with three unknowns and discusses solvability conditions. The third chapter focuses on Diophantine equations of the second degree. Linear Diophantine equations of??unknowns are discussed in the fourth chapter and two methods are introduced: the method of solving congruences and the method of reduction to a smaller number of unknowns. The Pythagorean trinity is introduced in the fifth chapter. In the sixth chapter, Fermat's equation, that is, the Diophantine equation above degree is presented and its solution is discussed. In the seventh chapter, linear Diophantine equations are solved similarly to the first chapter, but they are subjected to a stronger professional structure through definitions, theorems with proofs and algorithms. In addition, problems of Diophantine equations in????spaces are solved. Finally, in the eighth chapter systems of linear Diophantine congruences and systems of linear Diophantine equations are solved.