Representations Of Integers As Sums Of Fibonacci Squares

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Representations of Integers as Sums of Squares

Author : E. Grosswald
Publisher : Springer Science & Business Media
ISBN 13 : 1461385660
Total Pages : 262 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Representations of Integers as Sums of Squares by : E. Grosswald

Download or read book Representations of Integers as Sums of Squares written by E. Grosswald and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the academic year 1980-1981 I was teaching at the Technion-the Israeli Institute of Technology-in Haifa. The audience was small, but con sisted of particularly gifted and eager listeners; unfortunately, their back ground varied widely. What could one offer such an audience, so as to do justice to all of them? I decided to discuss representations of natural integers as sums of squares, starting on the most elementary level, but with the inten tion of pushing ahead as far as possible in some of the different directions that offered themselves (quadratic forms, theory of genera, generalizations and modern developments, etc.), according to the interests of the audience. A few weeks after the start of the academic year I received a letter from Professor Gian-Carlo Rota, with the suggestion that I submit a manuscript for the Encyclopedia of Mathematical Sciences under his editorship. I answered that I did not have a ready manuscript to offer, but that I could use my notes on representations of integers by sums of squares as the basis for one. Indeed, about that time I had already started thinking about the possibility of such a book and had, in fact, quite precise ideas about the kind of book I wanted it to be.

Fibonacci and Related Number Theoretic Tables: Fibonacci and related number theoretic tables

Author :
Publisher :
ISBN 13 :
Total Pages : 166 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Fibonacci and Related Number Theoretic Tables: Fibonacci and related number theoretic tables by :

Download or read book Fibonacci and Related Number Theoretic Tables: Fibonacci and related number theoretic tables written by and published by . This book was released on 1972 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fibonacci and Related Number Theoretical Tables

Author :
Publisher :
ISBN 13 :
Total Pages : 170 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Fibonacci and Related Number Theoretical Tables by :

Download or read book Fibonacci and Related Number Theoretical Tables written by and published by . This book was released on 1972 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fibonacci and Related Number Theoretical Tables

Author : Alfred Brousseau
Publisher :
ISBN 13 :
Total Pages : 176 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Fibonacci and Related Number Theoretical Tables by : Alfred Brousseau

Download or read book Fibonacci and Related Number Theoretical Tables written by Alfred Brousseau and published by . This book was released on 1972 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fibonacci’s Liber Abaci

Author : Laurence Sigler
Publisher : Springer Science & Business Media
ISBN 13 : 1461300797
Total Pages : 736 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Fibonacci’s Liber Abaci by : Laurence Sigler

Download or read book Fibonacci’s Liber Abaci written by Laurence Sigler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1202, Fibonacci’s Liber Abaci was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe. This is the first translation into a modern European language, of interest not only to historians of science but also to all mathematicians and mathematics teachers interested in the origins of their methods.

A Primer for the Fibonacci Numbers

Author : Marjorie Bicknell
Publisher :
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis A Primer for the Fibonacci Numbers by : Marjorie Bicknell

Download or read book A Primer for the Fibonacci Numbers written by Marjorie Bicknell and published by . This book was released on 1973 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fundamental Number Theory with Applications

Author : Richard A. Mollin
Publisher : CRC Press
ISBN 13 : 1420066617
Total Pages : 382 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Fundamental Number Theory with Applications by : Richard A. Mollin

Download or read book Fundamental Number Theory with Applications written by Richard A. Mollin and published by CRC Press. This book was released on 2008-02-21 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition • Removal of all advanced material to be even more accessible in scope • New fundamental material, including partition theory, generating functions, and combinatorial number theory • Expanded coverage of random number generation, Diophantine analysis, and additive number theory • More applications to cryptography, primality testing, and factoring • An appendix on the recently discovered unconditional deterministic polynomial-time algorithm for primality testing Taking a truly elementary approach to number theory, this text supplies the essential material for a first course on the subject. Placed in highlighted boxes to reduce distraction from the main text, nearly 70 biographies focus on major contributors to the field. The presentation of over 1,300 entries in the index maximizes cross-referencing so students can find data with ease.

Index to Mathematical Problems, 1975-1979

Author : Stanley Rabinowitz
Publisher : MathPro Press
ISBN 13 : 9780962640124
Total Pages : 548 pages
Book Rating : 4.6/5 (41 download)

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Book Synopsis Index to Mathematical Problems, 1975-1979 by : Stanley Rabinowitz

Download or read book Index to Mathematical Problems, 1975-1979 written by Stanley Rabinowitz and published by MathPro Press. This book was released on 1999 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Golden Ratio And Fibonacci Numbers

Author : Richard A Dunlap
Publisher : World Scientific
ISBN 13 : 9814496944
Total Pages : 170 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis The Golden Ratio And Fibonacci Numbers by : Richard A Dunlap

Download or read book The Golden Ratio And Fibonacci Numbers written by Richard A Dunlap and published by World Scientific. This book was released on 1997-12-16 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this invaluable book, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. In addition, the generation of the Fibonacci series and generalized Fibonacci series and their relationship to the golden ratio are presented. These concepts are applied to algorithms for searching and function minimization. The Fibonacci sequence is viewed as a one-dimensional aperiodic, lattice and these ideas are extended to two- and three-dimensional Penrose tilings and the concept of incommensurate projections. The structural properties of aperiodic crystals and the growth of certain biological organisms are described in terms of Fibonacci sequences.

Proofs that Really Count

Author : Arthur T. Benjamin
Publisher : American Mathematical Society
ISBN 13 : 1470472597
Total Pages : 210 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Proofs that Really Count by : Arthur T. Benjamin

Download or read book Proofs that Really Count written by Arthur T. Benjamin and published by American Mathematical Society. This book was released on 2022-09-21 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.

The Equations World

Author : Boris Pritsker
Publisher : Courier Dover Publications
ISBN 13 : 048684305X
Total Pages : 337 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis The Equations World by : Boris Pritsker

Download or read book The Equations World written by Boris Pritsker and published by Courier Dover Publications. This book was released on 2019-08-14 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Equations are the lifeblood of mathematics, science, and technology, and this book examines equations of all kinds. With his masterful ability to convey the excitement and elegance of mathematics, author Boris Pritsker explores equations from the simplest to the most complex—their history, their charm, and their usefulness in solving problems. The Equations World bridges the fields of algebra, geometry, number theory, and trigonometry, solving more than 280 problems by employing a wide spectrum of techniques. The author demystifies the subject with efficient hints, tricks, and methods that reveal the fun and satisfaction of problem solving. He also demonstrates how equations can serve as important tools for expressing a problem's data, showing the ways in which they assist in fitting parts together to solve the whole puzzle. In addition, brief historical tours reveal the foundations of mathematical thought by tracing the ideas and approaches developed by mathematicians over the centuries. Both recreational mathematicians and ambitious students will find this book an ample source of enlightenment and enjoyment.

Topics in the Theory of Numbers

Author : Janos Suranyi
Publisher : Springer Science & Business Media
ISBN 13 : 1461300150
Total Pages : 302 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Topics in the Theory of Numbers by : Janos Suranyi

Download or read book Topics in the Theory of Numbers written by Janos Suranyi and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number theory, the branch of mathematics that studies the properties of the integers, is a repository of interesting and quite varied problems, sometimes impossibly difficult ones. In this book, the authors have gathered together a collection of problems from various topics in number theory that they find beautiful, intriguing, and from a certain point of view instructive.

Applications of Fibonacci Numbers

Author : Fredric T. Howard
Publisher : Springer Science & Business Media
ISBN 13 : 9401142718
Total Pages : 390 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Applications of Fibonacci Numbers by : Fredric T. Howard

Download or read book Applications of Fibonacci Numbers written by Fredric T. Howard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains 33 papers from among the 41 papers presented at the Eighth International Conference on Fibonacci Numbers and Their Applications which was held at the Rochester Institute of Technology, Rochester, New York, from June 22 to June 26, 1998. These papers have been selected after a careful review by well known referees in the field, and they range from elementary number theory to probability and statistics. The Fibonacci numbers and recurrence relations are their unifying bond. It is anticipated that this book, like its seven predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. June 1, 1999 The Editor F. T. Howard Mathematics and Computer Science Wake Forest University Box 7388 Reynolda Station Winston-Salem, NC USA xvii THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Anderson, Peter G. , Chairman Horadam, A. F. (Australia), Co-Chair Arpaya, Pasqual Philippou, A. N. (Cyprus), Co-Chair Biles, John Bergum, G. E. (U. S. A. ) Orr, Richard Filipponi, P. (Italy) Radziszowski, Stanislaw Harborth, H. (Germany) Rich, Nelson Horibe, Y. (Japan) Howard, F. (U. S. A. ) Johnson, M. (U. S. A. ) Kiss, P. (Hungary) Phillips, G. M. (Scotland) Turner, J. (New Zealand) Waddill, M. E. (U. S. A. ) xix LIST OF CONTRIBUTORS TO THE CONFERENCE AGRATINI, OCTAVIAN, "Unusual Equations in Study. " *ANDO, SHIRO, (coauthor Daihachiro Sato), "On the Generalized Binomial Coefficients Defined by Strong Divisibility Sequences. " *ANATASSOVA, VASSIA K. , (coauthor J. C.

Applications of Fibonacci Numbers

Author : G.E. Bergum
Publisher : Springer Science & Business Media
ISBN 13 : 9400902239
Total Pages : 557 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Applications of Fibonacci Numbers by : G.E. Bergum

Download or read book Applications of Fibonacci Numbers written by G.E. Bergum and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains 43 papers form among the 55 papers presented at the Sixth International Conference on Fibonacci Numbers and Their Applications which was held at Washington State University, Pullman, Washington, from July 18-22, 1994. These papers have been selected after a careful review by well known referees in the field, and they range from elementary number theory to probability and statistics. The Fibonacci numbers and recurrence relations are their unifying bond. It is anticipated that this book, like its five predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. October 30, 1995 The Editors Gerald E. Bergum South Dakota State University Brookings, South Dakota, U.S.A. Alwyn F. Horadam University of New England Armidale, N.S.W., Australia Andreas N. Philippou 26 Atlantis Street Aglangia, Nicosia Cyprus xxi THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Long, Calvin T., Co-Chair Horadam, A.F. (Australia), Co-Chair Webb, William A., Co-Chair Philippou, A.N. (Cyprus), Co-Chair Burke, John Ando, S. (Japan) DeTemple, Duane W.

Applications of Fibonacci Numbers

Author : Fredric T. Howard
Publisher : Springer Science & Business Media
ISBN 13 : 0306485176
Total Pages : 328 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Applications of Fibonacci Numbers by : Fredric T. Howard

Download or read book Applications of Fibonacci Numbers written by Fredric T. Howard and published by Springer Science & Business Media. This book was released on 2004-02-29 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains 28 research articles from among the 49 papers and abstracts presented at the Tenth International Conference on Fibonacci Numbers and Their Applications. These articles have been selected after a careful review by expert referees, and they range over many areas of mathematics. The Fibonacci numbers and recurrence relations are their unifying bond. We note that the article "Fibonacci, Vern and Dan" , which follows the Introduction to this volume, is not a research paper. It is a personal reminiscence by Marjorie Bicknell-Johnson, a longtime member of the Fibonacci Association. The editor believes it will be of interest to all readers. It is anticipated that this book, like the eight predecessors, will be useful to research workers and students at all levels who are interested in the Fibonacci numbers and their applications. March 16, 2003 The Editor Fredric T. Howard Mathematics Department Wake Forest University Box 7388 Reynolda Station Winston-Salem, NC 27109 xxi THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Calvin Long, Chairman A. F. Horadam (Australia), Co-Chair Terry Crites A. N. Philippou (Cyprus), Co-Chair Steven Wilson A. Adelberg (U. S. A. ) C. Cooper (U. S. A. ) Jeff Rushal H. Harborth (Germany) Y. Horibe (Japan) M. Bicknell-Johnson (U. S. A. ) P. Kiss (Hungary) J. Lahr (Luxembourg) G. M. Phillips (Scotland) J. 'Thrner (New Zealand) xxiii xxiv LIST OF CONTRlBUTORS TO THE CONFERENCE * ADELBERG, ARNOLD, "Universal Bernoulli Polynomials and p-adic Congruences. " *AGRATINI, OCTAVIAN, "A Generalization of Durrmeyer-Type Polynomials. " BENJAMIN, ART, "Mathemagics.

The Fibonacci Quarterly

Author :
Publisher :
ISBN 13 :
Total Pages : 820 pages
Book Rating : 4.:/5 (37 download)

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Book Synopsis The Fibonacci Quarterly by :

Download or read book The Fibonacci Quarterly written by and published by . This book was released on 1984 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Sums of Squares of Integers

Author : Carlos J. Moreno
Publisher : CRC Press
ISBN 13 : 1584884568
Total Pages : 368 pages
Book Rating : 4.5/5 (848 download)

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Book Synopsis Sums of Squares of Integers by : Carlos J. Moreno

Download or read book Sums of Squares of Integers written by Carlos J. Moreno and published by CRC Press. This book was released on 2005-12-09 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a book of "firsts" - namely it is the first book to combine Liouville's elementary methods with the analytic methods of modular functions to study the representation of integers as sums of squares. It is the first book to tell how to compute the number of representations of an integer n as the sum of s squares of integers for any s and n. It is also the first book to give a proof of Szemeredi's theorem, and is the first number theory book to discuss how the modern theory of modular forms complements and clarifies the classical fundamental results about sums of squares. The book presents several existing, yet still interesting and instructive, examples of modular forms. Two chapters develop useful properties of the Bernoulli numbers and illustrate arithmetic progressions, proving the theorems of van der Waerden, Roth, and Szemeredi. The book also explains applications of the theory to three problems that lie outside of number theory in the areas of cryptanalysis, microwave radiation, and diamond cutting. The text is complemented by the inclusion of over one hundred exercises to test the reader's understanding.