Book•
Fibonacci and Lucas Numbers with Applications
01 Jan 2001-
TL;DR: The first 100 Lucas Numbers and their prime factorizations were given in this article, where they were shown to be a special case of the first 100 Fibonacci Numbers and Lucas Polynomials.
Abstract: Preface. List of Symbols. Leonardo Fibonacci. The Rabbit Problem. Fibonacci Numbers in Nature. Fibonacci Numbers: Additional Occurrances. Fibonacci and Lucas Identities. Geometric Paradoxes. Generalized Fibonacci Numbers. Additional Fibonacci and Lucas Formulas. The Euclidean Algorithm. Solving Recurrence Relations. Completeness Theorems. Pascal's Triangle. Pascal-Like Triangles. Additional Pascal-Like Triangles. Hosoya's Triangle. Divisibility Properties. Generalized Fibonacci Numbers Revisited. Generating Functions. Generating Functions Revisited. The Golden Ratio. The Golden Ratio Revisited. Golden Triangles. Golden Rectangles. Fibonacci Geometry. Regular Pentagons. The Golden Ellipse and Hyperbola. Continued Fractions. Weighted Fibonacci and Lucas Sums. Weighted Fibonacci and Lucas Sums Revisited. The Knapsack Problem. Fibonacci Magic Squares. Fibonacci Matrices. Fibonacci Determinants. Fibonacci and Lucas Congruences. Fibonacci and Lucas Periodicity. Fibonacci and Lucas Series. Fibonacci Polynomials. Lucas Polynomials. Jacobsthal Polynomials. Zeros of Fibonacci and Lucas Polynomials. Morgan-Voyce Polynomials. Fibonometry. Fibonacci and Lucas Subscripts. Gaussian Fibonacci and Lucas Numbers. Analytic Extensions. Tribonacci Numbers. Tribonacci Polynomials. Appendix 1: Fundamentals. Appendix 2: The First 100 Fibonacci and Lucas Numbers. Appendix 3: The First 100 Fibonacci Numbers and Their Prime Factorizations. Appendix 4: The First 100 Lucas Numbers and Their Prime Factorizations. References. Solutions to Odd-Numbered Exercises. Index.
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Book•
14 Mar 2005
TL;DR: This book brings together a vast body of results on matrix theory for easy reference and immediate application with hundreds of identities, inequalities, and matrix facts stated rigorously and clearly.
Abstract: "Matrix Mathematics" is a reference work for users of matrices in all branches of engineering, science, and applied mathematics. This book brings together a vast body of results on matrix theory for easy reference and immediate application. Each chapter begins with the development of relevant background theory followed by a large collection of specialized results. Hundreds of identities, inequalities, and matrix facts are stated rigorously and clearly with cross references, citations to the literature, and illuminating remarks. Twelve chapters cover all of the major topics in matrix theory: preliminaries; basic matrix properties; matrix classes and transformations; matrix polynomials and rational transfer functions; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; norms; functions of matrices and their derivatives; the matrix exponential and stability theory; and linear systems and control theory. A detailed list of symbols, a summary of notation and conventions, an extensive bibliography with author index, and an extensive index are provided for ease of use. The book will be useful for students at both the undergraduate and graduate levels, as well as for researchers and practitioners in all branches of engineering, science, and applied mathematics.
676 citations
Cites methods from "Fibonacci and Lucas Numbers with Ap..."
...In addition, matrices are widely used in rigid body mechanics [11,344,399,432,449,562], structural dynamics [350,409,467], fluid dynamics [137,200,595], circuit theory [13], queuing and stochastic systems [265,436], graph theory [202], signal processing [569], statistical mechanics [7,69,574], demography [329], optics [226], and number theory [339]....
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Book•
26 Mar 2006
TL;DR: This website is an invitation to modern number theory that will be your best choice for better reading book and you can take the book as a source to make better concept.
Abstract: Give us 5 minutes and we will show you the best book to read today. This is it, the an invitation to modern number theory that will be your best choice for better reading book. Your five times will not spend wasted by reading this website. You can take the book as a source to make better concept. Referring the books that can be situated with your needs is sometime difficult. But here, this is so easy. You can find the best thing of book that you can read.
175 citations
TL;DR: The Lucas numbers as discussed by the authors are a close relative of the Fibonacci numbers and have achieved a kind of celebrity status, referred to as the "two shining stars in the vast array of integer sequences".
Abstract: Among numerical sequences, the Fibonacci numbers Fn have achieved a kind of celebrity status. Indeed, Koshy gushingly refers to them as one of the "two shining stars in the vast array of integer sequences" [16, p. xi]. The second of Koshy's "shining stars" is the Lucas numbers, a close relative of the Fibonacci numbers, about which we will say more below. The Fibonacci numbers are famous for possessing wonderful and amazing properties. Some are well known. For example, the sums and differences of Fibonacci numbers are Fibonacci numbers, and the ratios of Fibonacci numbers converge to the golden mean. Others are less familiar. Did you know that any four consecutive Fibonacci numbers can be combined to form a Pythagorean triple? Or how about this: The greatest common divisor of two Fibonacci numbers is another Fibonacci number. More precisely, the gcd of F, and Fm is Fk, where k is the gcd of n and m.
165 citations
Cites background or methods from "Fibonacci and Lucas Numbers with Ap..."
...As a case in point, Koshy [16] has devoted nearly 700 pages to the properties of Fibonacci and Lucas numbers, with scarcely a mention of general two-term recurrences....
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...The version given above, (wz, 2xy, yz − wx), appears in Koshy [16] with a 1968 attribution to Umansky and Tallman....
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...We have included page references from Koshy [16]....
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TL;DR: In this paper, the authors investigated the Fibonacci and Lucas quaternions and derived the generating functions and Binet formulas for these two types of quadratic functions. And they also derived some sums formulas for them.
Abstract: In this paper, we investigate the Fibonacci and Lucas quaternions. We give the generating functions and Binet formulas for these quaternions. Moreover, we derive some sums formulas for them.
163 citations
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TL;DR: The book as mentioned in this paper is designed for a first course in number theory with minimal prerequisites and is designed to stimulate curiosity about numbers and their properties, including almost a thousand imaginative exercises and problems.
Abstract: Designed for a first course in number theory with minimal prerequisites, the book is designed to stimulates curiosity about numbers and their properties. Includes almost a thousand imaginative exercises and problems.
809 citations
Book•
01 Jan 1953
TL;DR: In this paper, the authors present a Chronological Table of Cultural Connections: The Hunters of the Savanna (The Stone Age), Numeral Systems, the Agricultural Revolution (The Cradles of Civilization). Babylonian and Egyptian Mathematics.
Abstract: Before the 17th Century. Part I: Cultural Connections: The Hunters of the Savanna (The Stone Age). Numeral Systems. Part II: Cultural Connections: The Agricultural Revolution (The Cradles of Civilization). Babylonian and Egyptian Mathematics. Part III: Cultural Connections: The Philosophers of the Agora (Hellenic Greece). Phytagorean Mathematics. Duplication, Trisection, And Quadrature. Part IV: Cultural Connections: The Oikoumene (The Persian Empire, Hellenistic Greece, And the Roman Empire). Euclid and His Elements. Greek Mathematics After Euclid. Part V: Cultural Connections: The Asian Empires (China, India, And the Rise of Islam). Chinese, Hindu, And Arabian Mathematics. Part VI: Cultural Connections: Serfs, Lords, And Popes (The European Middle Ages). European Mathematics, 500 to 1600. The 17th Century and After. Part VII: Cultural Connections: Puritans and Sea Dogs (The Expansion of Europe). The Dawn of Modern Mathematics. Analytic Geometry and Other Precalculus Developments. The Calculus and Related Concepts. Part VIII: Cultural Connections: The Revolt of the Middle Class (The 18th Century in Europe and America). The 18th Century and the Exploitation of the Calculus. Part IX: Cultural Connections (The Industrial Revolution (The 19th Century). The Early 19th Century and the Liberation of Geometry and Algebra. The Late 19th Century and the Arithmetization of Analysis. Part X: Cultural Connections: The Atom and the Spinnnig Wheel (The 20th Century). Transition Into the 20th Century. General Bibliography. A Chronological Table. Answers and Suggestions for the Solutions of the Problem Studies. Index.
487 citations
TL;DR: The topics covered are: additive representation functions, the Erdős-Fuchs theorem, multiplicative problems (involving general sequences), additive and multiplicative Sidon sets, hybrid problems (i.e., problems involving both special and general sequences, arithmetic functions and the greatest prime factor func- tion and mixed problems.
Abstract: 68 unsolved problems and conjectures in number theory are presented and brie y discussed. The topics covered are: additive representation functions, the Erdős-Fuchs theorem, multiplicative problems (involving general sequences), additive and multiplicative Sidon sets, hybrid problems (i.e., problems involving both special and general sequences), arithmetic functions, the greatest prime factor func- tion and mixed problems.
425 citations
"Fibonacci and Lucas Numbers with Ap..." refers background in this paper
...[90] D.M. Burton, Elementary Number Theory, 3rd edition, W.C. Brown, Dubuque, Iowa, 1989....
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...[461] C.S. Ogilvy and J.T. Anderson, Excursions in Number Theory, Dover, New York, 1966....
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...[454] T. Nagel, Introduction to Number Theory, Chelsea, New York, 1964....
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...[369] T. Koshy, Elementary Number Theory with Applications, 2nd edition, Elsevier, Boston, Mass., 2007....
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...In fact, at the 1969 Summer Institute of Number Theory at Stony Brook, New York, H.M. Stark of the University of Michigan at Ann Arbor asked: Which Fibonacci numbers have this distinct property?...
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Book•
01 Mar 1991
TL;DR: Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra.
Abstract: Wed, 28 Nov 2018 02:13:00 GMT linear algebra with applications 7th pdf Academia.edu is a platform for academics to share research papers. Fri, 07 Dec 2018 02:03:00 GMT Linear Algebra with Applications 7th.PDF | Irene ren ... Introductory linear algebra by bernard kolman 7th edition pdf . Download Introductory linear algebra with applications 7th edition ... Fri, 07 Dec 2018 08:01:00 GMT Introductorylinearalgebraby bernardkolman7theditionpd f.pdf ... Free step-by-step solutions to Linear Algebra with Applications (9780136009290) Slader Fri, 07 Dec 2018 01:27:00 GMT Linear Algebra with Applications (9780136009290 ... LINEAR ALGEBRA Jim Hefferon ... Applications. ... In the rest of this book we will solve linear systems by bringing them to!! Sun, 09 Dec 2018 21:06:00 GMT Linear Algebra Book Joshua Nicholson Solution for Linear Algebra 7th edition. by peter_li ... mathematical statistics with applications (7th edition).pdf. ... to three linear equations in the ... Wed, 05 Dec 2018 09:29:00 GMT Nicholson Solution for Linear Algebra 7th edition ... Why is Chegg Study better than downloaded Linear Algebra With Applications 7th Edition PDF solution manuals? It's easier to figure out tough problems faster using ... Sat, 08 Dec 2018 05:15:00 GMT Linear Algebra With Applications 7th Edition ... Chegg Linear Algebra Larson 7th Edition.pdf. Linear Algebra Larson 7th Edition.pdf. Sign In. Details Main menu ... Sun, 09 Dec 2018 18:21:00 GMT Linear Algebra Larson 7th Edition.pdf Google Drive Linear Algebra with Applications (Steven Leon) Huajun Huang ... Express a linear system as the form ax= b. ... Simple Matching Searches p54 in 7th ed, (skip if no time). Sun, 25 Nov 2018 16:57:00 GMT Linear Algebra with Applications (Steven Leon) Linear Algebra and Its Applications Fourth Edition Gilbert Strang y ... 1.2 The Geometry of Linear Equations ... linear algebra: ... Sun, 09 Dec 2018 21:49:00 GMT Linear Algebra and Its Applications (Fourth Edition) Linear Algebra with Applications 7th. Edition [Steven J. Leon] on Amazon.com. *FREE* shipping on qualifying offers. book has 517 pages plus 3 pages of index so it has ... Mon, 10 Dec 2018 02:28:00 GMT Linear Algebra with Applications 7th. Edition: Steven J ... Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra ... PDF ... Mon, 26 Nov 2018 04:39:00 GMT Linear Algebra and Its Applications Official Site A First Course in Linear Algebra ... applications of linear algebra to graph theory. ... Systems of Linear Equations 1 What is Linear Algebra ... Fri, 07 Dec 2018 16:22:00 GMT Exercise and Solution Manual for A First ... Linear Algebra Buy Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory)) on Amazon.com FREE SHIPPING on qualified orders Tue, 04 Dec 2018 11:10:00 GMT Linear Algebra with Applications (9th Edition) (Featured ... interests include the applications of linear algebra to graph theory. ... Systems of Linear Equations1 What is Linear Algebra ... by daggers in the PDF and ... Sun, 09 Dec 2018 13:42:00 GMT Download as a PDF A First Course in ... Linear Algebra Gilbert Strang – Linear Algebra (PDF) Wed, 05 Dec 2018 19:30:00 GMT Gilbert Strang – Linear Algebra (PDF) Leon Linear Algebra With Applications 7th Pdf mediafire links free download, download Linear Algebra with Applications, Steven J Leon, 8th, Linear Algebra with ... Mon, 10 Dec 2018 09:59:00 GMT Leon Linear Algebra With Applications 7th Pdf AbeBooks.com: Linear Algebra with Applications (7th Edition) (9780131857858) by Steven J. Leon and a great selection of similar New,
317 citations
"Fibonacci and Lucas Numbers with Ap..." refers background in this paper
...Since similar matrices have the same trace and determinant [58], it follows that trace(An) = αn + βn = Ln = Fn+1 + Fn−1 = trace(Qn)....
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...So there is a total of 7 = L4 closed paths of length 4 in G: 11111 11121 11211 12111 12121 21112 21212 This leads us to two interesting observations; but first, two definitions from linear algebra [58]....
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