Download or read book On the Smarandache function and the Fermat number written by Jinrui Wang and published by Infinite Study. This book was released on with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: For any positive integer n, the famous F.Smarandache function S(n) is defined as the smallest positive integer m such that n | m!.

Download or read book On the pseudo Smarandache function written by Henry Ibstedt and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study originates from questions posed on alternating iterations involving the pseudo-Smarandache function Z(n) and the Euler function. Interesting questions have been resolved through the surprising involvement of Fermat numbers

Download or read book Conjectures on Primes and Fermat Pseudoprimes Many Based on Smarandache Function written by Marius Coman and published by Infinite Study. This book was released on with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book An Introduction to the Smarandache Function written by Charles Ashbacher and published by Infinite Study. This book was released on 1995 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Math Encyclopedia of Smarandache type Notions written by Marius Coman and published by Infinite Study. This book was released on with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book A survey on Smarandache notions in number theory I Smarandache function written by Huaning Liu and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we give a survey on recent results on Smarandache function.

Download or read book Smarandache Function Journal vol 9 1998 written by V. Seleacu and published by Infinite Study. This book was released on with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc.

Download or read book Smarandache Function Journal vol 12 2001 written by Charles Ashbacher and published by Infinite Study. This book was released on with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc.

Download or read book TWO HUNDRED AND THIRTEEN CONJECTURES ON PRIMES written by Marius Coman and published by Infinite Study. This book was released on 2015-02-15 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: In two of my previous published books, “Two hundred conjectures and one hundred and fifty open problems on Fermat pseudoprimes”, respectively “Conjectures on primes and Fermat pseudoprimes, many based on Smarandache function”, I already expressed my passion for integer numbers, especially for primes and Fermat pseudoprimes, fascinating numbers that seem to be a little bit more willing to let themselves ordered and understood than the prime numbers.

Download or read book The Smarandache Function written by Constantin Dumitrescu and published by Infinite Study. This book was released on 1996-01-01 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Smarandache Function Vol 1 written by R. Muller and published by Infinite Study. This book was released on 2000-08-01 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Smarandache function, say S, is a numerical function defined such that for every positive integer n, its image S(n) is the smallest positive integer whole factorial is divisible by n.

Download or read book 17 Lectures on Fermat Numbers written by Michal Krizek and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The pioneering work of Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book provides an overview of the many properties of Fermat numbers and demonstrates their applications in areas such as number theory, probability theory, geometry, and signal processing. It is an ideal introduction to the basic mathematical ideas and algebraic methods connected with the Fermat numbers.

Download or read book The Smarandache Korselt criterion a variant of Korselt s criterion written by Marius Coman and published by Infinite Study. This book was released on with total page 3 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining two of my favourite objects of study, the Fermat pseudoprimes and the Smarandache function, I was able to formulate a criterion, inspired by Korselt’s criterion for Carmichael numbers and by Smarandache function, which seems to be necessary (though not sufficient as the Korselt’s criterion for absolute Fermat pseudoprimes) for a composite number (without a set of probably definable exceptions) to be a Fermat pseudoprime to base two.

Download or read book A Set of New Smarandache Functions Sequences and Conjectures written by Felice Russo and published by Infinite Study. This book was released on 2000 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Smarandache Notions Vol 12 Proceedings of the Second International Conference on Smarandache Type Notions in Mathematics and Quantum Physics written by Leonardo Motta and published by Infinite Study. This book was released on 2001-01-01 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Applications of Smarandache Function Prime and Coprime Functions written by Sebastián Martín Ruiz and published by Infinite Study. This book was released on 2001 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Algorithm for Calculating Smarandache s Function and Wich Using Legendre s Formula written by Tatiana-Corina Dosescu and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.