## Pell and Pell–Lucas Numbers with ApplicationsPell 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 | |

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 |

417 | |

423 | |