This book discusses special properties of integer sequences from a unique point of view. It generalizes common, well-known properties and connects them with sequences such as divisible sequences, Lucas sequences, Lehmer sequences, periods of sequences, lifting properties, and so on. The book presents theories derived by using elementary means and includes results not usually found in common number theory books. Considering the impact and usefulness of these theorems, the book also aims at being valuable for Olympiad level problem solving as well as regular research. This book will be of interest to students, researchers and faculty members alike.

Discusses special properties of integer sequences from a unique point of view Focuses on divisible sequences, Lucas sequences, Lehmer sequences, periods of sequences, and lifting properties of sequences Appeals to Olympiad students, researchers and anyone interested in Fibonacci number

Autorentext

Masum Billal is working as a senior data scientist in Dhaka, Bangladesh. He has authored a book on number theory and he has been a trainer at math camps of Bangladesh for 5/6 years. His research interests include mathematics (specially number theory), machine learning, cryptography, etc. Samin Riasat has completed his Master of Mathematics in Computer Science at the University of Waterloo, Canada. He has authored a book on mathematical olympiads and his research articles have been published in journals of repute. He is also a reviewer for Mathematical Reviews.

Inhalt

1.Preliminaries.- 2.Linear Recurrent Sequences.- 3.Divisible Sequences.- 4.Lucas Sequences.- 5.Lehmer Sequences.- 6.On Primitive Divisors.