Mersenne Numbers And Fermat Numbers

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Mersenne Numbers And Fermat Numbers

Elena Deza
Mersenne Numbers And Fermat Numbers Book PDF

Author : Elena Deza
Publisher : World Scientific
Page : 327 pages
File Size : 41,8 Mb
Release : 2021-08-06
Category : Mathematics
ISBN : 9789811230332

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Mersenne Numbers And Fermat Numbers by Elena Deza Pdf

This book contains a complete detailed description of two classes of special numbers closely related to classical problems of the Theory of Primes. There is also extensive discussions of applied issues related to Cryptography.In Mathematics, a Mersenne number (named after Marin Mersenne, who studied them in the early 17-th century) is a number of the form Mn = 2n - 1 for positive integer n.In Mathematics, a Fermat number (named after Pierre de Fermat who first studied them) is a positive integer of the form Fn = 2k+ 1, k=2n, where n is a non-negative integer.Mersenne and Fermat numbers have many other interesting properties. Long and rich history, many arithmetic connections (with perfect numbers, with construction of regular polygons etc.), numerous modern applications, long list of open problems allow us to provide a broad perspective of the Theory of these two classes of special numbers, that can be useful and interesting for both professionals and the general audience.

17 Lectures on Fermat Numbers

Michal Krizek,Florian Luca,Lawrence Somer
17 Lectures on Fermat Numbers Book PDF

Author : Michal Krizek,Florian Luca,Lawrence Somer
Publisher : Springer Science & Business Media
Page : 280 pages
File Size : 49,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9780387218502

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17 Lectures on Fermat Numbers by Michal Krizek,Florian Luca,Lawrence Somer Pdf

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.

Elementary Theory of Numbers

W. Sierpinski
Elementary Theory of Numbers Book PDF

Author : W. Sierpinski
Publisher : Elsevier
Page : 513 pages
File Size : 55,6 Mb
Release : 1988-02-01
Category : Mathematics
ISBN : 9780080960197

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Elementary Theory of Numbers by W. Sierpinski Pdf

Since the publication of the first edition of this work, considerable progress has been made in many of the questions examined. This edition has been updated and enlarged, and the bibliography has been revised. The variety of topics covered here includes divisibility, diophantine equations, prime numbers (especially Mersenne and Fermat primes), the basic arithmetic functions, congruences, the quadratic reciprocity law, expansion of real numbers into decimal fractions, decomposition of integers into sums of powers, some other problems of the additive theory of numbers and the theory of Gaussian integers.

The Book of Prime Number Records

Paulo Ribenboim
The Book of Prime Number Records Book PDF

Author : Paulo Ribenboim
Publisher : Springer Science & Business Media
Page : 496 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468405071

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The Book of Prime Number Records by Paulo Ribenboim Pdf

This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquim series established to honor Professors A. J. Coleman and H. W. Ellis and to acknow ledge their long lasting interest in the quality of teaching under graduate students. In another colloquim lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guilllless Book oj Records, remainded me very gently that the most "innumerate" people of the world are of a certain tribe in Mato Grosso, Brazil. They do not even have a word to express the number "two" or the concept of plurality. "Yes Morris, I'm from Brazil, but my book will contain numbers different from 'one.' " He added that the most boring 800-page book is by two Japanese mathematicians (whom I'll not name), and consists of about 16 million digits of the number 11. "I assure you Morris, that in spite of the beauty of the apparent randomness of the decimal digits of 11, I'll be sure that my text will include also some words." Acknowledgment. The manuscript of this book was prepared on the word processor by Linda Nuttall. I wish to express my appreciation for the great care, speed, and competence of her work.

A Concrete Introduction to Higher Algebra

Lindsay N. Childs
A Concrete Introduction to Higher Algebra Book PDF

Author : Lindsay N. Childs
Publisher : Springer Science & Business Media
Page : 592 pages
File Size : 43,7 Mb
Release : 2008-11-26
Category : Mathematics
ISBN : 9780387745275

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A Concrete Introduction to Higher Algebra by Lindsay N. Childs Pdf

This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. The new examples and theory are built in a well-motivated fashion and made relevant by many applications - to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises are found throughout the book.

The New Book of Prime Number Records

Paulo Ribenboim
The New Book of Prime Number Records Book PDF

Author : Paulo Ribenboim
Publisher : Springer Science & Business Media
Page : 558 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207597

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The New Book of Prime Number Records by Paulo Ribenboim Pdf

This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium senes. In another colloquium lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guinness Book of Records, reminded me very gently that the most "innumerate" people of the world are of a certain trible in Mato Grosso, Brazil. They do not even have a word to express the number "two" or the concept of plurality. "Yes, Morris, I'm from Brazil, but my book will contain numbers different from ·one.''' He added that the most boring 800-page book is by two Japanese mathematicians (whom I'll not name) and consists of about 16 million decimal digits of the number Te. "I assure you, Morris, that in spite of the beauty of the appar ent randomness of the decimal digits of Te, I'll be sure that my text will include also some words." And then I proceeded putting together the magic combina tion of words and numbers, which became The Book of Prime Number Records. If you have seen it, only extreme curiosity could impel you to have this one in your hands. The New Book of Prime Number Records differs little from its predecessor in the general planning. But it contains new sections and updated records.

Invitation to Number Theory: Second Edition

Oystein Ore
Invitation to Number Theory Second Edition Book PDF

Author : Oystein Ore
Publisher : American Mathematical Soc.
Page : 134 pages
File Size : 46,6 Mb
Release : 2017-12-29
Category : Number theory
ISBN : 9780883856536

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Invitation to Number Theory: Second Edition by Oystein Ore Pdf

Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, … and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and many more. In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat's Last Theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises.

How Euler Did Even More

C. Edward Sandifer
How Euler Did Even More Book PDF

Author : C. Edward Sandifer
Publisher : The Mathematical Association of America
Page : 254 pages
File Size : 44,7 Mb
Release : 2014-11-19
Category : Mathematics
ISBN : 9780883855843

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How Euler Did Even More by C. Edward Sandifer Pdf

Sandifer has been studying Euler for decades and is one of the world’s leading experts on his work. This volume is the second collection of Sandifer’s “How Euler Did It” columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler’s clever inventiveness and Sandifer’s wonderful ability to explicate and put it all in context.

My Numbers, My Friends

Paulo Ribenboim
My Numbers My Friends Book PDF

Author : Paulo Ribenboim
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 46,8 Mb
Release : 2006-05-10
Category : Mathematics
ISBN : 9780387227542

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My Numbers, My Friends by Paulo Ribenboim Pdf

This selection of expository essays by Paulo Ribenboim should be of interest to mathematicians from all walks. Ribenboim, a highly praised author of several popular titles, writes each essay in a light and humorous language without secrets, making them thoroughly accessible to everyone with an interest in numbers. This new collection includes essays on Fibonacci numbers, prime numbers, Bernoulli numbers, and historical presentations of the main problems pertaining to elementary number theory, such as Kummers work on Fermat's last theorem.

Prime Numbers

David Wells
Prime Numbers Book PDF

Author : David Wells
Publisher : Turner Publishing Company
Page : 260 pages
File Size : 51,9 Mb
Release : 2011-01-13
Category : Mathematics
ISBN : 9781118045718

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Prime Numbers by David Wells Pdf

A fascinating journey into the mind-bending world of prime numbers Cicadas of the genus Magicicada appear once every 7, 13, or 17 years. Is it just a coincidence that these are all prime numbers? How do twin primes differ from cousin primes, and what on earth (or in the mind of a mathematician) could be sexy about prime numbers? What did Albert Wilansky find so fascinating about his brother-in-law's phone number? Mathematicians have been asking questions about prime numbers for more than twenty-five centuries, and every answer seems to generate a new rash of questions. In Prime Numbers: The Most Mysterious Figures in Math, you'll meet the world's most gifted mathematicians, from Pythagoras and Euclid to Fermat, Gauss, and Erd?o?s, and you'll discover a host of unique insights and inventive conjectures that have both enlarged our understanding and deepened the mystique of prime numbers. This comprehensive, A-to-Z guide covers everything you ever wanted to know--and much more that you never suspected--about prime numbers, including: * The unproven Riemann hypothesis and the power of the zeta function * The "Primes is in P" algorithm * The sieve of Eratosthenes of Cyrene * Fermat and Fibonacci numbers * The Great Internet Mersenne Prime Search * And much, much more

13 Lectures on Fermat's Last Theorem

Paulo Ribenboim
13 Lectures on Fermat s Last Theorem Book PDF

Author : Paulo Ribenboim
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 50,8 Mb
Release : 1979-12-18
Category : Computers
ISBN : 0387904328

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13 Lectures on Fermat's Last Theorem by Paulo Ribenboim Pdf

Fermat's problem, also ealled Fermat's last theorem, has attraeted the attention of mathematieians far more than three eenturies. Many clever methods have been devised to attaek the problem, and many beautiful theories have been ereated with the aim of proving the theorem. Yet, despite all the attempts, the question remains unanswered. The topie is presented in the form of leetures, where I survey the main lines of work on the problem. In the first two leetures, there is a very brief deseription of the early history , as well as a seleetion of a few of the more representative reeent results. In the leetures whieh follow, I examine in sue­ eession the main theories eonneeted with the problem. The last two lee tu res are about analogues to Fermat's theorem. Some of these leetures were aetually given, in a shorter version, at the Institut Henri Poineare, in Paris, as well as at Queen's University, in 1977. I endeavoured to produee a text, readable by mathematieians in general, and not only by speeialists in number theory. However, due to a limitation in size, I am aware that eertain points will appear sketehy. Another book on Fermat's theorem, now in preparation, will eontain a eonsiderable amount of the teehnieal developments omitted here. It will serve those who wish to learn these matters in depth and, I hope, it will clarify and eomplement the present volume.

Prime Numbers: The Holy Grail Of Mathematics

Thamer Naouech
Prime Numbers The Holy Grail Of Mathematics Book PDF

Author : Thamer Naouech
Publisher : Thamer Naouech
Page : 46 pages
File Size : 45,8 Mb
Release : 2020-10-20
Category : Juvenile Nonfiction
ISBN : 9798697533154

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Prime Numbers: The Holy Grail Of Mathematics by Thamer Naouech Pdf

It is undeniable how prime numbers are one of the most beautiful and fascinating topics in mathematics. But what are prime numbers? Are they only numbers that are divisible by 1 and themselves, or do they have another interesting hidden face?Throughout history, the mystery of prime numbers has challenged the greatest minds in mathematics starting from Euclid of Alexandria to Fermat, Euler, Gauss, and Erdős,… who attempted to solve the puzzling problem of primes. The achievements they realized and the secrets they revealed can only assert how deep the concept of prime numbers is. Starting from how prime numbers exist in nature, and how they are of great use in modern cryptography on which our daily life completely depends, the author travels in the holy kingdom of primes diving into some conjectures involving those special numbers. From the Riemann Hypothesis and the well-known zeta function, he explains how a note in the margin turned to be Fermat’s Last Theorem, one of the most important problems in the history of mathematics. From Mersenne Primes, he gets to the twin primes, those shining little stars in the blue sky of primes. And from Euclid’s proof of the infinite number of primes he gets to a hidden pattern in the distribution of primes discovered by Stanisław Ulam and called the Ulam Spiral. After this little trip, you will know, dear reader, why prime numbers deserve to be called "the holy grail of mathematics".

Introduction to Cryptography

Sahadeo Padhye,Rajeev A. Sahu,Vishal Saraswat
Introduction to Cryptography Book PDF

Author : Sahadeo Padhye,Rajeev A. Sahu,Vishal Saraswat
Publisher : CRC Press
Page : 185 pages
File Size : 42,9 Mb
Release : 2018-09-04
Category : Computers
ISBN : 9781351628136

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Introduction to Cryptography by Sahadeo Padhye,Rajeev A. Sahu,Vishal Saraswat Pdf

Electronic communication and financial transactions have assumed massive proportions today. But they come with high risks. Achieving cyber security has become a top priority, and has become one of the most crucial areas of study and research in IT. This book introduces readers to perhaps the most effective tool in achieving a secure environment, i.e. cryptography. This book offers more solved examples than most books on the subject, it includes state of the art topics and discusses the scope of future research.

The Little Book of Bigger Primes

Paulo Ribenboim
The Little Book of Bigger Primes Book PDF

Author : Paulo Ribenboim
Publisher : Springer Science & Business Media
Page : 250 pages
File Size : 51,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475743302

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The Little Book of Bigger Primes by Paulo Ribenboim Pdf

This book could have been called "Selections from the Book of Prime Number Records." However, I prefered the title which propelled you on the first place to open it, and perhaps (so I hope) to buy it! Richard K. Guy, with his winning ways, suggested the title to me, and I am grateful. But the book isn't very different from its parent. Like a bonsai, which has all the main characteristics of the full-sized tree, this little paperback should exert the same fatal attraction. I wish it to be as dangerous as the other one, in the saying of John Brillhart. I wish that you, young student, teacher or retired mathematician, engineer, computer buff, all of you who are friends of numbers, to be driven into thinking about the beautiful theory of prime numbers, with its inherent mystery. I wish you to exercise your brain and fingers-not vice-versa. But I do not wish you, specialist in number theory to look at this little book-most likely you have been eliminated from this shorter version-what a terrible feeling. But do not cry, you had your book already. This one is for those who will be taking over and should put their steps forward, mostly little, occasionally giant, to develop the science of numbers. Paulo Ribenboim Contents Preface vii Guiding the Reader xii Index of Notations xiii Introduction 1 1 How Many Prime Numbers Are There? 3 I. Euclid's Proof .. 3 11. Kummer's Proof 4 II. P6lya's Proof . .

Approximately Calculus

Shahriar Shahriari
Approximately Calculus Book PDF

Author : Shahriar Shahriari
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 49,7 Mb
Release : 2006
Category : Approximation theory
ISBN : 9780821837504

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Approximately Calculus by Shahriar Shahriari Pdf

Is there always a prime number between $n$ and $2n$? Where, approximately, is the millionth prime? And just what does calculus have to do with answering either of these questions? It turns out that calculus has a lot to do with both questions, as this book can show you. The theme of the book is approximations. Calculus is a powerful tool because it allows us to approximate complicated functions with simpler ones. Indeed, replacing a function locally with a linear--or higher order--approximation is at the heart of calculus. The real star of the book, though, is the task of approximating the number of primes up to a number $x$. This leads to the famous Prime Number Theorem--and to the answers to the two questions about primes. While emphasizing the role of approximations in calculus, most major topics are addressed, such as derivatives, integrals, the Fundamental Theorem of Calculus, sequences, series, and so on. However, our particular point of view also leads us to many unusual topics: curvature, Pade approximations, public key cryptography, and an analysis of the logistic equation, to name a few. The reader takes an active role in developing the material by solving problems. Most topics are broken down into a series of manageable problems, which guide you to an understanding of the important ideas. There is also ample exposition to fill in background material and to get you thinking appropriately about the concepts. Approximately Calculus is intended for the reader who has already had an introduction to calculus, but wants to engage the concepts and ideas at a deeper level. It is suitable as a text for an honors or alternative second semester calculus course.