**Thesis Type:** Postgraduate

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

**Approval Date:** 2011

**Thesis Language:** Turkish

**Student:** HATİCE ALKAN

**Supervisor: **AHMET TEKCAN

In this thesis, some algebraic properties of binary quadratic forms and Diophantine equations are given.The thesis consists of five chapters. In the first chapter, the preliminary notations, definitions and theorems which are to be used in later chapters are given.In the second chapter, the number of rational points on some specific curves is formulated over finite fields .In the third chapter, the integer solutions of Diophantine equation are considered both over integers and over finite fields . Later the number of rational points on curves related to roots of are determined over .In the fourth chapter, quadratic ideals and indefinite binary quadratic forms are considered. Here two specific kuadratik ideal are considered and derived some properties of them. Later their product is obtained. Finally, some properties of indefinite binary quadratic forms related to these ideals are obtained.In the last chapter, some properties of a specific integer sequence are given and later integer solutions of a Pell equation related to parameters of this integer sequence are formulated. Also some recurrence relations on this integer sequence are given.