Add to Book Shelf
Flag as Inappropriate
Email this Book

Geometric Theorems, Diophantine Equations, And Arithmetic Functions

By József Sándor

Click here to view

Book Id: WPLBN0002097093
Format Type: pdf
File Size: 1,027 KB
Reproduction Date: 9/1/2011

Title: Geometric Theorems, Diophantine Equations, And Arithmetic Functions  
Author: József Sándor
Language: English
Subject: Non Fiction, Education, Smarandache Collections
Collections: Mathematics, Geometry, Mathematical Analysis, Arithmetic, Math, Authors Community, Literature, Most Popular Books in China, Favorites in India, Education
Publication Date:
Publisher: American Research Press
Member Page: Florentin Smarandache


APA MLA Chicago

Sándor, J. (n.d.). Geometric Theorems, Diophantine Equations, And Arithmetic Functions. Retrieved from

This book contains short notes or articles, as well as studies on several topics of Geometry and Number theory. The material is divided into ve 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. 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-Kalm ar lemma, with many applications. Article 20 may be considered also as an introduction to Chapter 3 on Arithmetic functions. Here many papers study the famous Smarandache function, the source of inspiration of so many mathematicians or scientists working in other elds. The author has discovered various generalizations, extensions, or analogues functions. Other topics are connected to the composition of arithmetic functions, arithmetic functions at factorials, Dedekind's or Pillai's functions, as well as semigroup-valued multiplicative functions. Chapter 4 discusses certain divisibility problems or questions related especially to the sequence of prime numbers. The author has solved various conjectures by Smarandache, Bencze, Russo etc.; see especially articles 4,5,7,8,9,10. Finally, Chapter 5 studies certain irrationality criteria; some of them giving interesting results on series involving the Smarandache function. Article 3.13 (i.e. article 13 in Chapter 3) is concluded also with a theorem of irrationality on a dual of the pseudo-Smarandache function.


Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.