A Set Of New Smarandache Functions Sequences And Conjectures
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A Set Of New Smarandache Functions Sequences And Conjectures
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Author : Felice Russo
language : en
Publisher: Infinite Study
Release Date : 2000
A Set Of New Smarandache Functions Sequences And Conjectures written by Felice Russo and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Smarandache function categories.
Generalized Partitions And New Ideas On Number Theory And Smarandache Sequences
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Author : Amarnath Murthy
language : en
Publisher: Infinite Study
Release Date : 2005-01-01
Generalized Partitions And New Ideas On Number Theory And Smarandache Sequences written by Amarnath Murthy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
Florentin Smarandache is an incredible source of ideas, only some of which are mathematical in nature. Amarnath Murthy has published a large number of papers in the broad area of Smarandache Notions, which are math problems whose origin can be traced to Smarandache. This book is an edited version of many of those papers, most of which appeared in Smarandache Notions Journal, and more information about SNJ is available at http://www.gallup.unm.edu/~smarandache/ . The topics covered are very broad, although there are two main themes under which most of the material can be classified. A Smarandache Partition Function is an operation where a set or number is split into pieces and together they make up the original object. For example, a Smarandache Repeatable Reciprocal partition of unity is a set of natural numbers where the sum of the reciprocals is one. The first chapter of the book deals with various types of partitions and their properties and partitions also appear in some of the later sections.The second main theme is a set of sequences defined using various properties. For example, the Smarandache n2n sequence is formed by concatenating a natural number and its double in that order. Once a sequence is defined, then some properties of the sequence are examined. A common exploration is to ask how many primes are in the sequence or a slight modification of the sequence. The final chapter is a collection of problems that did not seem to be a precise fit in either of the previous two categories. For example, for any number d, is it possible to find a perfect square that has digit sum d? While many results are proven, a large number of problems are left open, leaving a great deal of room for further exploration.
A Set Of New Smarandache Functions Sequences And Conjectures In Number Theory
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Author : Felice Russo
language : en
Publisher:
Release Date : 2000
A Set Of New Smarandache Functions Sequences And Conjectures In Number Theory written by Felice Russo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Smarandache notions categories.
A Set Of New Smarandache Functions Sequences And Conjectures In Number Theory
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Author : Felice Russo
language : en
Publisher:
Release Date :
A Set Of New Smarandache Functions Sequences And Conjectures In Number Theory written by Felice Russo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Sequences Of Integers Conjectures And New Arithmetical Tools Collected Papers
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Author : Marius Coman
language : en
Publisher: Infinite Study
Release Date : 2015-01-01
Sequences Of Integers Conjectures And New Arithmetical Tools Collected Papers written by Marius Coman and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-01 with Mathematics categories.
Part One of this book of collected papers brings together papers regarding conjectures on primes, twin primes, squares of primes, semiprimes, different types of pairs of primes, recurrent sequences, other sequences of integers related to primes created through concatenation and in other ways. Part Two brings together several articles presenting the notions of c-primes, m-primes, c-composites and m-composites (c/m integers), also the notions of g-primes, s-primes, g-composites and s-composites (g/s integers) and show some of the applications of these notions. Part Three presents the notions of “Mar constants” and “Smarandache-Coman constants”, useful to highlight the periodicity of some infinite sequences of positive integers (sequences of squares, cubes, triangualar numbers) , respectively in the analysis of Smarandache concatenated sequences. Part Four presents the notion of Smarandache-Coman sequences, id est the sequences of primes formed through different arithmetical operations on the terms of Smarandache concatenated sequences. Part Five presents the notion of Smarandache-Coman function, a function based on the Smarandache function which seems to be particularly interesting: beside other notable characteristics, it seems to have as values all the prime numbers and, more than that, they seem to appear, leaving aside the non-prime values, in natural order. This book of collected papers seeks to expand the knowledge on some well known classes of numbers and also to define new classes of primes or classes of integers directly related to primes.
The Math Encyclopedia Of Smarandache Type Notions
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Author : Marius Coman
language : en
Publisher: Infinite Study
Release Date :
The Math Encyclopedia Of Smarandache Type Notions written by Marius Coman and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
About the works of Florentin Smarandache have been written a lot of books (he himself wrote dozens of books and articles regarding math, physics, literature, philosophy). Being a globally recognized personality in both mathematics (there are countless functions and concepts that bear his name) and literature, it is natural that the volume of writings about his research is huge. What we try to do with this encyclopedia is to gather together as much as we can both from Smarandache’s mathematical work and the works of many mathematicians around the world inspired by the Smarandache notions. We structured this book using numbered Definitions, Theorems, Conjectures, Notes and Comments, in order to facilitate an easier reading but also to facilitate references to a specific paragraph. We divided the Bibliography in two parts, Writings by Florentin Smarandache (indexed by the name of books and articles) and Writings on Smarandache notions (indexed by the name of authors). We treated, in this book, about 130 Smarandache type sequences, about 50 Smarandache type functions and many solved or open problems of number theory. We also have, at the end of this book, a proposal for a new Smarandache type notion, id est the concept of “a set of Smarandache-Coman divisors of order k of a composite positive integer n with m prime factors”, notion that seems to have promising applications, at a first glance at least in the study of absolute and relative Fermat pseudoprimes, Carmichael numbers and Poulet numbers. This encyclopedia is both for researchers that will have on hand a tool that will help them “navigate” in the universe of Smarandache type notions and for young math enthusiasts: many of them will be attached by this wonderful branch of mathematics, number theory, reading the works of Florentin Smarandache.
Smarandache Unsolved Problems And New Progress In Chinese Language
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Author : Editors: Liu Yanni, Li Ling, Liu Baoli
language : en
Publisher: Infinite Study
Release Date : 2008
Smarandache Unsolved Problems And New Progress In Chinese Language written by Editors: Liu Yanni, Li Ling, Liu Baoli and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
New improved results of the research in Chinese language on Smarandache¿s codification used in computer programming, smarandacheials, totient and congruence functions, sequences, irrational constants in number theory, multi-space and geometries.
Smarandache Function Journal Vol 14 2004
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Author : Sabin Tabirca
language : en
Publisher: Infinite Study
Release Date :
Smarandache Function Journal Vol 14 2004 written by Sabin Tabirca and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc.
Sequences Of Primes Obtained By The Method Of Concatenation Collected Papers
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Author : Marius Coman
language : en
Publisher: Infinite Study
Release Date : 2016
Sequences Of Primes Obtained By The Method Of Concatenation Collected Papers written by Marius Coman and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.
The purpose of this book is to show that the method of concatenation can be a powerful tool in number theory and, in particular, in obtaining possible infinite sequences of primes. Part One of this book, “Primes in Smarandache concatenated sequences and Smarandache-Coman sequences of primes” , contains 12 papers on various sequences of primes that are distinguished among the terms of the well known Smarandache concatenated sequences. The sequences presented in this part are related to concatenation in three different ways: the sequence is obtained by the method of concatenation but the operation applied on its terms is some other arithmetical operation; the sequence is not obtained by concatenation but the operation applied on its terms is concatenation or both the sequence and the operation applied on its terms (in order to find sequences of primes) are using the method of concatenation. Part Two of this book, “Sequences of primes obtained by the method of concatenation” brings together 51 articles which aim, using the mentioned method, to highlight sequences of numbers which are rich in primes or are liable to lead to large primes. The method of concatenation is applied to different classes of numbers, e.g. Poulet numbers, twin primes, reversible primes, triangular numbers, repdigits, factorial numbers, fibonorial numbers, primordial numbers in order to obtain sequences of primes.
Conjectures On Primes And Fermat Pseudoprimes Many Based On Smarandache Function
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Author : Marius Coman
language : en
Publisher: Infinite Study
Release Date :
Conjectures On Primes And Fermat Pseudoprimes Many Based On Smarandache Function written by Marius Coman and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
It is always difficult to talk about arithmetic, because those who do not know what is about, nor do they understand in few sentences, no matter how inspired these might be, and those who know what is about, do no need to be told what is about. Arithmetic is that branch of mathematics that you keep it in your soul and in your mind, not in your suitcase or laptop. Part One of this book of collected papers aims to show new applications of Smarandache function in the study of some well known classes of numbers, like Sophie Germain primes, Poulet numbers, Carmichael numbers ets. Beside the well-known notions of number theory, we defined in these papers the following new concepts: “Smarandache-Coman divisors of order k of a composite integer n with m prime factors”, “Smarandache-Coman congruence on primes”, “Smarandache-Germain primes”, Coman-Smarandache criterion for primality”, “Smarandache-Korselt criterion”, “Smarandache-Coman constants”. Part Two of this book brings together several papers on few well known and less known types of primes.