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Start Over Author "Sándor, József" Topic number theory
7 results on '"Sándor, József"'

1. GEOMETRIC THEOREMS, DIOPHANTINE EQUATIONS, AND ARITHMETIC FUNCTIONS

Author

Sándor, József

Subjects
Number theory, Smarandache function
Abstract

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 numbersand functions; and Some irrationality results. Chapter 1 deals essentially with geometricinequalities for the remarkable elements of triangles or tetrahedrons. Other themes havean arithmetic character (as 9-12) on number theoretic problems in Geometry. Chapter 2includes various diophantine equations, some of which are treatable by elementary methods;others are partial solutions of certain unsolved problems. An important method isbased on the famous Euler-Bell-Kalmar lemma, with many applications. Article 20 maynbsp;be considered also as an introduction to Chapter 3 on Arithmetic functions. Here manynbsp;papers study the famous Smarandache function, the source of inspiration of so manynbsp;mathematicians or scientists working in other elds. The author has discovered variousnbsp;generalizations, extensions, or analogues functions./p>

Published
2002
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2. On an Arithmetic Inequality.

Author

Sándor, József

Subjects
*ARITHMETIC, *MATHEMATICAL equivalence, *NUMBER systems, *NUMBER theory, *MATHEMATICS
Abstract

We obtain an arithmetic proof and a refinement of the inequality ϕ ( nk) + σ k( n) < 2 nk, where n ≧ 2 and k ≧ 2. An application to another inequality is also provided. [ABSTRACT FROM AUTHOR]

Published
2014
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3. A note on f-minimum functions.

Author

Sándor, József

Subjects
*ARITHMETIC functions, *FACTOR tables, *PERFECT numbers, *SMARANDACHE function, *PRIME numbers, *PROOF theory, *SET theory, *NUMBER theory, *MATHEMATICAL logic
Abstract

For a given arithmetical function f : N → N, let F : N → N be defined by F(n) = min{m ⩾ : n∣f(m)}, if this exists. Such functions, introduced in [4], will be called as the f-minimum functions. If f satisfies the property a ⩽ b ⇒ f(a)∣f(b), we shall prove that F(ab) = max{F(a), F(b)} for (a; b) = 1. For a more restrictive class of functions, we will determine F(n) where n is an even perfect number. These results are generalizations of theorems from [10], [1], [3], [6]. [ABSTRACT FROM AUTHOR]

Published
2009

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