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Definitions Solved And Unsolved Problems Conjectures And Theorems In Number Theory And Geometry


Definitions Solved And Unsolved Problems Conjectures And Theorems In Number Theory And Geometry
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Definitions Solved And Unsolved Problems Conjectures And Theorems In Number Theory And Geometry


Definitions Solved And Unsolved Problems Conjectures And Theorems In Number Theory And Geometry
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 1999-12-01

Definitions Solved And Unsolved Problems Conjectures And Theorems In Number Theory And Geometry written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-01 with Mathematics categories.




The Math Encyclopedia Of Smarandache Type Notions


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.



Solved And Unsolved Problems In Number Theory


Solved And Unsolved Problems In Number Theory
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Author : Daniel Shanks
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-24

Solved And Unsolved Problems In Number Theory written by Daniel Shanks and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-24 with Mathematics categories.


The investigation of three problems, perfect numbers, periodic decimals, and Pythagorean numbers, has given rise to much of elementary number theory. In this book, Daniel Shanks, past editor of Mathematics of Computation, shows how each result leads to further results and conjectures. The outcome is a most exciting and unusual treatment. This edition contains a new chapter presenting research done between 1962 and 1978, emphasizing results that were achieved with the help of computers.



Unsolved Problems In Number Theory


Unsolved Problems In Number Theory
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Author : Richard Guy
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

Unsolved Problems In Number Theory written by Richard Guy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.


To many laymen, mathematicians appear to be problem solvers, people who do "hard sums". Even inside the profession we dassify ouselves as either theorists or problem solvers. Mathematics is kept alive, much more than by the activities of either dass, by the appearance of a succession of unsolved problems, both from within mathematics itself and from the increasing number of disciplines where it is applied. Mathematics often owes more to those who ask questions than to those who answer them. The solution of a problem may stifte interest in the area around it. But "Fermat 's Last Theorem", because it is not yet a theorem, has generated a great deal of "good" mathematics, whether goodness is judged by beauty, by depth or by applicability. To pose good unsolved problems is a difficult art. The balance between triviality and hopeless unsolvability is delicate. There are many simply stated problems which experts tell us are unlikely to be solved in the next generation. But we have seen the Four Color Conjecture settled, even if we don't live long enough to learn the status of the Riemann and Goldbach hypotheses, of twin primes or Mersenne primes, or of odd perfect numbers. On the other hand, "unsolved" problems may not be unsolved at all, or than was at first thought.



Thirty Six Unsolved Problems In Number Theory


Thirty Six Unsolved Problems In Number Theory
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date :

Thirty Six Unsolved Problems In Number Theory written by Florentin Smarandache 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.


Partially or totally unsolved questions in number theory and geometry especially, such as coloration problems, elementary geometric conjectures, partitions, generalized periods of a number, length of a generalized period, arithmetic and geometric progressions are exposed.



Smarandache Unsolved Problems And New Progress In Chinese Language


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.



Geometric Theorems And Arithmetic Functions


Geometric Theorems And Arithmetic Functions
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Author : József Sándor
language : en
Publisher: Infinite Study
Release Date : 2002

Geometric Theorems And Arithmetic Functions written by József Sándor and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.




Unfolding The Labyrinth Open Problems In Physics Mathematics Astrophysics And Other Areas Of Science


Unfolding The Labyrinth Open Problems In Physics Mathematics Astrophysics And Other Areas Of Science
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2006-01-01

Unfolding The Labyrinth Open Problems In Physics Mathematics Astrophysics And Other Areas Of Science written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-01 with Mathematics categories.


Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astrophysics, geophysics etc. It is of our hope that some of the problems discussed in this book will find their place either in theoretical exploration or further experiments, while some parts of these problems may be found useful for scholarly stimulation.The present book is also intended for young physics and mathematics fellows who will perhaps find the unsolved problems described here are at least worth pondering. If this book provides only a few highlights of plausible solutions, it is merely to keep the fun of readers in discovering the answers by themselves. Bon voyage!



Generalized Partitions And New Ideas On Number Theory And Smarandache Sequences


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.



Geometric Theorems Diophantine Equations And Arithmetic Functions


Geometric Theorems Diophantine Equations And Arithmetic Functions
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Author : J. Sándor
language : en
Publisher: Infinite Study
Release Date : 2002

Geometric Theorems Diophantine Equations And Arithmetic Functions written by J. Sándor and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Arithmetic functions categories.