قضایای هندسی، معادلات دیوفانتین و توابع حسابی سندور

This book contains short notes and articles, as well as studies on several topics of Geometry and Number Theory. The material is divided into five chapters: Geometric theorems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers and functions; and Some irrationality results. Many papers study the Smarandache type functions and Pseudo-Smarandache function, conjectures. This book contains short notes or articles, as well as studies on several topics of Geometry and Number theory. The material is divided into five chapters: Geometric theorems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers and functions; and Some irrationality results. Chapter 1 deals essentially with geometric inequalities for the remarkable elements of triangles or tetrahedrons, such as Smarandache's Pedal Triangle. Other themes have an arithmetic character (as 9-12) on number theoretic problems in Geometry. Chapter 2 includes various Diophantine equations, some of which are treatable by elementary methods; others are partial solutions of certain unsolved problems. An important method is based on the famous Euler-Bell-Kalmár lemma, with many applications. Article 20 may be considered also as an introduction to Chapter 3 on Arithmetic functions. Here many papers study the Smarandache Series and the famous Smarandache function, the source of inspiration of so many mathematicians or scientists working in other fields.