**Thesis Type:** Postgraduate

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

**Approval Date:** 2019

**Thesis Language:** Turkish

**Student:** Arzu Akın

**Supervisor: **Ahmet Tekcan

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.