**Thesis Type:** Postgraduate

**Institution Of The Thesis:** Uludağ Üniversitesi, Turkey

**Approval Date:** 2017

**Thesis Language:** Turkish

**Student:** AZİZ YAZLA

**Supervisor: **AHMET TEKCAN

In this work, some algebraic properties of generalized balancing numbers, namely t −balancing numbers and their relationships with Pell, Pell-Lucas and square triangular numbers are considered. In the first section, some preliminary notations, definitions and theorems which are to be used in later sections are given. In the second section, balancing numbers, their some algebraic properties, their relationships with Pell and Pell-Lucas numbers, companion matrices and some specific balancing functions are considered. In the third section which is the original part of the thesis, we first determine the set of all positive integer solutions of the Pell equation 2x2 − y2 = 2t 2 −1. Later we obtain the general terms of all t −balancing numbers, their Binet formulas. We also deduce some theorems concerning the relationships between t −balancing numbers and Pell, Pell- Lucas and square triangular numbers.