On the solvability of an equation involving the Smarandache function and Euler function PDF Download
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Author: Weiguo Duan
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 10
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Book Description
For any positive integer n, the famous F.Smarandache function S(n) is defined as the smallest positive integer m such that n divides m!.
Author: Weiguo Duan
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 10
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Book Description
For any positive integer n, the famous F.Smarandache function S(n) is defined as the smallest positive integer m such that n divides m!.
Author: A. A. K. Majumdar
Publisher: Infinite Study
ISBN: 159973124X
Category : Mathematics
Languages : en
Pages : 217
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Book Description
This book covers only a part of the wide and diverse field of the Smarandache Notions, andcontains some of the materials that I gathered as I wandered in the world of Smarandache. Mostof the materials are already published in different journals, but some materials are new andappear for the first time in this book. All the results are provided with proofs._ Chapter 1 gives eleven recursive type Smarandache sequences, namely, the SmarandacheOdd, Even, Prime Product, Square Product (of two types), Higher Power Product (of twotypes), Permutation, Circular, Reverse, Symmetric and Pierced Chain sequences_ Chapter 2 deals with the Smarandache Cyclic Arithmetic Determinant and BisymmetricArithmetic Determinant sequences, and series involving the terms of the Smarandachebisymmetric determinant natural and bisymmetric arithmetic determinant sequences_ Chapter 3 treats the Smarandache function S(n)_ Chapter 4 considers, in rather more detail, the pseudo Smarandache function Z(n)_ And the Smarandache S-related and Z-related triangles are the subject matter of Chapter 5.To make the book self-contained, some well-known results of the classical Number Theory aregiven in Chapter 0. In order to make the book up-to-date, the major results of other researchersare also included in the book.At the end of each chapter, several open problems are given.
Author: Zhang Wenpeng
Publisher: Infinite Study
ISBN: 1599730642
Category :
Languages : en
Pages : 132
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Book Description
Papers on two problems related to the Smarandache function, the additive k-power complements, the generalization of sequence of numbers with alternate common differences, an equation related to the Smarandache function and its positive integer solutions, the pseudo Smarandache square-free function, and other similar topics. Contributors: W. Zhang, Y. Guo, W. Xiong, S. Yilmaz, M. Turgut, A. A. Majumdar, B. Ahmad, J. Zhang, P. Zhang, N. Dung, and many others.
Author: Zhang Wenpeng
Publisher: Infinite Study
ISBN: 159973088X
Category : Mathematics
Languages : en
Pages : 143
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Book Description
Author: Wenpeng Zhang
Publisher: Infinite Study
ISBN: 1599731274
Category : Mathematics
Languages : en
Pages : 151
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Book Description
This Book is devoted to the proceedings of the Sixth International Conferenceon Number Theory and Smarandache Notions held in Tianshui during April 24-25,2010. The organizers were Prof. Zhang Wenpeng and Prof. Wangsheng He from Tianshui Normal University. The conference was supported by Tianshui Normal University and there were more than 100 participants.
Author: W. B. Vasantha Kandasamy, Florentin Smarandache, K. Ilanthenral
Publisher: Infinite Study
ISBN: 1599730057
Category : Mathematics
Languages : en
Pages : 352
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Book Description
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 1194
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Book Description
Author: Richard Crandall
Publisher: Springer Science & Business Media
ISBN: 0387289798
Category : Mathematics
Languages : en
Pages : 597
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Book Description
Bridges the gap between theoretical and computational aspects of prime numbers Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects Authors are well-known and highly-regarded in the field
Author:
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 816
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Book Description
Author: SABUROU SAITOH
Publisher: Scientific Research Publishing, Inc. USA
ISBN: 1649970897
Category : Mathematics
Languages : en
Pages : 203
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Book Description
The common sense on the division by zero with the long and mysterious history is wrong and our basic idea on the space around the point at infinity is also wrong since Euclid. On the gradient or on differential coefficients we have a great missing since tan(π/2) = 0. Our mathematics is also wrong in elementary mathematics on the division by zero. In this book in a new and definite sense, we will show and give various applications of the division by zero 0/0 = 1/0 = z/0 = 0. In particular, we will introduce several fundamental concepts in calculus, Euclidean geometry, analytic geometry, complex analysis and differential equations. We will see new properties on the Laurent expansion, singularity, derivative, extension of solutions of differential equations beyond analytical and isolated singularities, and reduction problems of differential equations. On Euclidean geometry and analytic geometry, we will find new fields by the concept of the division by zero. We will collect many concrete properties in mathematical sciences from the viewpoint of the division by zero. We will know that the division by zero is our elementary and fundamental mathematics.
