An Algorithm for Calculating Smarandache's Function and Wich Using Legendre's Formula
An Algorithm for Calculating Smarandache's Function and Wich Using Legendre's Formula

Author: Tatiana-Corina Dosescu

Publisher: Infinite Study

Published:

Total Pages: 10

ISBN-13:

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The paper presents a calculation algorithm for the values of the function S, defined by Fl. Smarandache [6], [1], [4], [5], an algorithm that uses the writing of numbers in base ten and it is based on Legendre's formula and some theoretical results. It differs from the one presented in [8], which avoids factorization, and from the one presented in [6], which requires writing on a generalized basis. Then a characterization of a prime number is given. Finally, a numerical application is presented.The paper presents a calculation algorithm for the values of the function S, defined by Fl. Smarandache [6], [1], [4], [5], an algorithm that uses the writing of numbers in base ten and it is based on Legendre's formula and some theoretical results. It differs from the one presented in [8], which avoids factorization, and from the one presented in [6], which requires writing on a generalized basis. Then a characterization of a prime number is given. Finally, a numerical application is presented.

Various Arithmetic Functions and their Applications
Various Arithmetic Functions and their Applications

Author: Octavian Cira

Publisher: Infinite Study

Published: 2016

Total Pages: 402

ISBN-13: 1599733722

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Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc. on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes squares cubes factorials, almost primes, mobile periodicals, functions, tables, prime square factorial bases, generalized factorials, generalized palindromes, so on, have been extracted from the Archives of American Mathematics (University of Texas at Austin) and Arizona State University (Tempe): "The Florentin Smarandache papers" special collections, and Arhivele Statului (Filiala Vâlcea & Filiala Dolj, Romania). This book was born from the collaboration of the two authors, which started in 2013. The first common work was the volume "Solving Diophantine Equations", published in 2014. The contribution of the authors can be summarized as follows: Florentin Smarandache came with his extraordinary ability to propose new areas of study in number theory, and Octavian Cira - with his algorithmic thinking and knowledge of Mathcad.

Prime Numbers
Prime Numbers

Author: Richard Crandall

Publisher: Springer Science & Business Media

Published: 2006-04-07

Total Pages: 597

ISBN-13: 0387289798

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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

The Prime Numbers and Their Distribution
The Prime Numbers and Their Distribution

Author: Gerald Tenenbaum

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 137

ISBN-13: 0821816470

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One notable new direction this century in the study of primes has been the influx of ideas from probability. The goal of this book is to provide insights into the prime numbers and to describe how a sequence so tautly determined can incorporate such a striking amount of randomness. The book opens with some classic topics of number theory. It ends with a discussion of some of the outstanding conjectures in number theory. In between are an excellent chapter on the stochastic properties of primes and a walk through an elementary proof of the Prime Number Theorem. This book is suitable for anyone who has had a little number theory and some advanced calculus involving estimates. Its engaging style and invigorating point of view will make refreshing reading for advanced undergraduates through research mathematicians.

Handbook of Number Theory I
Handbook of Number Theory I

Author: József Sándor

Publisher: Springer Science & Business Media

Published: 2005-11-17

Total Pages: 638

ISBN-13: 1402042159

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This handbook covers a wealth of topics from number theory, special attention being given to estimates and inequalities. As a rule, the most important results are presented, together with their refinements, extensions or generalisations. These may be applied to other aspects of number theory, or to a wide range of mathematical disciplines. Cross-references provide new insight into fundamental research. Audience: This is an indispensable reference work for specialists in number theory and other mathematicians who need access to some of these results in their own fields of research.

Elementary Number Theory in Nine Chapters
Elementary Number Theory in Nine Chapters

Author: James J. Tattersall

Publisher: Cambridge University Press

Published: 1999-10-14

Total Pages: 420

ISBN-13: 9780521585316

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This book is intended to serve as a one-semester introductory course in number theory. Throughout the book a historical perspective has been adopted and emphasis is given to some of the subject's applied aspects; in particular the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises have been included. It is assumed that the reader will have 'pencil in hand' and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject.

The Distribution of Prime Numbers
The Distribution of Prime Numbers

Author: Albert Edward Ingham

Publisher: Cambridge University Press

Published: 1990-09-28

Total Pages: 140

ISBN-13: 9780521397896

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Originally published in 1934, this volume presents the theory of the distribution of the prime numbers in the series of natural numbers. Despite being long out of print, it remains unsurpassed as an introduction to the field.

Business & Management Practices
Business & Management Practices

Author: Duygu Fırat

Publisher: IJOPEC PUBLICATION

Published: 2019-12-18

Total Pages: 342

ISBN-13: 1912503875

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Businesses are important for economic development of nation and increasing of living standards of people. Also, management is a critical factor for both businesses because it creates utility for businesses. All the success and failure depend upon business functions and management. In this context, this book contains three important factors of business management. In the first part of the book covers strategic management subjects; especially entrepreneurship and human resource management. The second part of the book includes accounting and auditing. The third part of the book is about marketing.