Integer Sequences: Divisibility, Lucas and Lehmer Sequences

Preface
	References
Who This Book Is For
Contents
About the Authors
1 Preliminaries
	1.1 Groups, Rings, Fields, and Vector Spaces
		1.1.1 Groups
		1.1.2 Rings and Fields
		1.1.3 Vector Spaces
	1.2 Matrices
	1.3 Polynomials
	1.4 Cyclotomic Polynomials
	References
2 Linear Recurrent Sequences
	2.1 Introduction
	2.2 Periodicity
	2.3 Fundamental Theorems on Periodicity
	2.4 Finding Pre-Period and Least Period
	References
3 Divisibility Sequences
	3.1 Introduction
	3.2 Characterization of Divisibility Sequences
	3.3 Binomial Coefficients
	References
4 Lucas Sequences
	4.1 Introduction
	4.2 Divisibility of Second-Order Lucas Sequences
	4.3 Lucas Sequence of Arbitrary Order
	References
5 Lehmer Sequences
	5.1 Introduction
	5.2 Divisibility of Lehmer Sequence
	5.3 Periodicity of Lehmer Sequence
	5.4 Extending Wilson\'s Theorem
	5.5 LCM Sequence of Lehmer Sequences
	5.6 Subsequence of Lehmer Sequences
	References
6 On Primitive Divisors
	6.1 The History of Primitive Divisors
	6.2 Primitive Divisors of an-bn
	6.3 Primitive Divisors of Real Lucas Sequences
	6.4 Primitive Divisors of Real Lehmer Sequences
	6.5 Primitive Divisors of Complex Lehmer Sequences
	References
7 Exercises
	Reference
Appendix  Glossary
	References
Index