# Pell and Pell–Lucas Numbers with Applications

Springer, Nov 11, 2014 - Mathematics - 431 pages

Pell and Pell–Lucas numbers, like the well-known Fibonacci and Catalan numbers, continue to intrigue the mathematical world with their beauty and applicability. They offer opportunities for experimentation, exploration, conjecture, and problem-solving techniques, connecting the fields of analysis, geometry, trigonometry, and various areas of discrete mathematics, number theory, graph theory, linear algebra, and combinatorics. Pell and Pell–Lucas numbers belong to an extended Fibonacci family as a powerful tool for extracting numerous interesting properties of a vast array of number sequences.

A key feature of this work is the historical flavor that is interwoven into the extensive and in-depth coverage of the subject. An interesting array of applications to combinatorics, graph theory, geometry, and intriguing mathematical puzzles is another highlight engaging the reader. The exposition is user-friendly, yet rigorous, so that a broad audience consisting of students, math teachers and instructors, computer scientists and other professionals, along with the mathematically curious will all benefit from this book.

Finally, Pell and Pell–Lucas Numbers provides enjoyment and excitement while sharpening the reader’s mathematical skills involving pattern recognition, proof-and-problem-solving techniques.

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### Contents

 1 Fundamentals 1 2 Pells Equation 31 3 Continued Fractions 57 4 Pythagorean Triples 79 5 Triangular Numbers 87 6 SquareTriangular Numbers 101 7 Pell and PellLucas Numbers 115 8 Additional Pell Identities 151
 13 Pell Triangles 247 14 Pell and PellLucas Polynomials 255 15 Pellonometry 282 16 Pell Tilings 303 17 PellFibonacci Hybridities 325 18 An Extended Pell Family 363 19 Chebyshev Polynomials 371 20 Chebyshev Tilings 395

 9 Pascals Triangle and the Pell Family 173 10 Pell Sums and Products 193 11 Generating Functions for the Pell Family 207 12 Pell Walks 227
 Appendix 411 References 417 Index 423 Copyright

### About the author (2014)

Thomas Koshy is Professor Emeritus of Mathematics at Framingham State University in Framingham, Massachusetts. In 2007, he received the Faculty of the Year Award and his publication Fibonacci and Lucas numbers with Applications won the Association of American Publishers' new book award in 2001. Professor Koshy has also authored numerous articles on a wide spectrum of topics and more than seven books, among them, Elementary Number Theory with Applications, second edition; Catalan Numbers with Applications; Triangular Arrays with Applications; and Discrete Mathematics with Applications.