Download or read book Mersenne Numbers And Fermat Numbers written by Elena Deza and published by World Scientific. This book was released on 2021-08-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 How Euler Did Even More written by C. Edward Sandifer and published by The Mathematical Association of America. This book was released on 2014-11-19 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Prime Numbers written by David Wells and published by Turner Publishing Company. This book was released on 2011-01-13 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Number Theory and Its History written by Oystein Ore and published by Courier Corporation. This book was released on 2012-07-06 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.
Download or read book Elementary Theory of Numbers written by W. Sierpinski and published by Elsevier. This book was released on 1988-02-01 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The New Book of Prime Number Records written by Paulo Ribenboim and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Selection of Problems in the Theory of Numbers written by Waclaw Sierpinski and published by Elsevier. This book was released on 2014-05-16 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Selection of Problems in the Theory of Numbers focuses on mathematical problems within the boundaries of geometry and arithmetic, including an introduction to prime numbers. This book discusses the conjecture of Goldbach; hypothesis of Gilbreath; decomposition of a natural number into prime factors; simple theorem of Fermat; and Lagrange's theorem. The decomposition of a prime number into the sum of two squares; quadratic residues; Mersenne numbers; solution of equations in prime numbers; and magic squares formed from prime numbers are also elaborated in this text. This publication is a good reference for students majoring in mathematics, specifically on arithmetic and geometry.
Download or read book The Book of Prime Number Records written by Paulo Ribenboim and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Concrete Introduction to Higher Algebra written by Lindsay N. Childs and published by Springer Science & Business Media. This book was released on 2008-11-26 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Prime Numbers and Computer Methods for Factorization written by Hans Riesel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the modern age of almost universal computer usage, practically every individual in a technologically developed society has routine access to the most up-to-date cryptographic technology that exists, the so-called RSA public-key cryptosystem. A major component of this system is the factorization of large numbers into their primes. Thus an ancient number-theory concept now plays a crucial role in communication among millions of people who may have little or no knowledge of even elementary mathematics. The independent structure of each chapter of the book makes it highly readable for a wide variety of mathematicians, students of applied number theory, and others interested in both study and research in number theory and cryptography.
Download or read book Primes of the Form x2 ny2 written by David A. Cox and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern number theory began with the work of Euler and Gauss to understand and extend the many unsolved questions left behind by Fermat. In the course of their investigations, they uncovered new phenomena in need of explanation, which over time led to the discovery of field theory and its intimate connection with complex multiplication. While most texts concentrate on only the elementary or advanced aspects of this story, Primes of the Form x2 + ny2 begins with Fermat and explains how his work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. Further, the book shows how the results of Euler and Gauss can be fully understood only in the context of class field theory. Finally, in order to bring class field theory down to earth, the book explores some of the magnificent formulas of complex multiplication. The central theme of the book is the story of which primes p can be expressed in the form x2 + ny2. An incomplete answer is given using quadratic forms. A better though abstract answer comes from class field theory, and finally, a concrete answer is provided by complex multiplication. Along the way, the reader is introduced to some wonderful number theory. Numerous exercises and examples are included. The book is written to be enjoyed by readers with modest mathematical backgrounds. Chapter 1 uses basic number theory and abstract algebra, while chapters 2 and 3 require Galois theory and complex analysis, respectively.
Download or read book Excursions in Number Theory written by Charles Stanley Ogilvy and published by Courier Corporation. This book was released on 1988-01-01 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No special training is needed, just high school mathematics and an inquisitive mind. "A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers." — Martin Gardner.
Download or read book The Mathematical Career of Pierre de Fermat 1601 1665 written by Michael Sean Mahoney and published by Princeton University Press. This book was released on 1994 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hailed as one of the greatest mathematical results of the twentieth century, the recent proof of Fermat's Last Theorem by Andrew Wiles brought to public attention the enigmatic problem-solver Pierre de Fermat, who centuries ago stated his famous conjecture in a margin of a book, writing that he did not have enough room to show his "truly marvelous demonstration." Along with formulating this proposition--xn+yn=zn has no rational solution for n > 2--Fermat, an inventor of analytic geometry, also laid the foundations of differential and integral calculus, established, together with Pascal, the conceptual guidelines of the theory of probability, and created modern number theory. In one of the first full-length investigations of Fermat's life and work, Michael Sean Mahoney provides rare insight into the mathematical genius of a hobbyist who never sought to publish his work, yet who ranked with his contemporaries Pascal and Descartes in shaping the course of modern mathematics.
Download or read book Prime Numbers The Holy Grail Of Mathematics written by Thamer Naouech and published by Thamer Naouech. This book was released on 2020-10-20 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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".
Download or read book Those Fascinating Numbers written by Jean-Marie De Koninck and published by American Mathematical Soc.. This book was released on 2009 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: Who would have thought that listing the positive integers along with their most remarkable properties could end up being such an engaging and stimulating adventure? The author uses this approach to explore elementary and advanced topics in classical number theory. A large variety of numbers are contemplated: Fermat numbers, Mersenne primes, powerful numbers, sublime numbers, Wieferich primes, insolite numbers, Sastry numbers, voracious numbers, to name only a few. The author also presents short proofs of miscellaneous results and constantly challenges the reader with a variety of old and new number theory conjectures. This book becomes a platform for exploring new concepts such as the index of composition and the index of isolation of an integer. In addition, the book displays several tables of particular families of numbers, including the list of all 88 narcissistic numbers and the list of the eight known numbers which are not prime powers but which can be written as the sum of the cubes of their prime factors, and in each case with the algorithm used to create them.
Download or read book Prime Numbers written by Richard Crandall and published by Springer Science & Business Media. This book was released on 2006-04-07 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
