Two special integer sequences and their relationship with pell and balancing numbers


Thesis Type: Postgraduate

Institution Of The Thesis: Bursa Uludağ University, Fen Bilimleri Enstitüsü, Turkey

Approval Date: 2019

Thesis Language: Turkish

Student: Arzu Akın

Supervisor: AHMET TEKCAN

Abstract:

In this work, two special integer sequences and are defined and some algebraic relations on them are derived. Furthermore, the relationship between and Pell, Pell-Lucas also balancing numbers are studied. In the first section, some preliminary notations, definitions and theorems related to in-teger sequences which are to be used in later sections are given. In the second section, the integer sequence which derived from the sum of first non-zero terms of Pell numbers is defined and obtained some algebraic rela-tions on it. Later its relationship with Pell, Pell-Lucas and balancing numbers is con-sidered. In the last section, all positive integer solutions of the Pell equation for an integer is obtained by a different method and defined a new integer sequence derived from this Pell equation and obtained some algebra-ic relations on it.