Recurrence sequences and applications


Thesis Type: Doctorate

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

Approval Date: 2015

Thesis Language: Turkish

Student: Buse Uzatıcı

Supervisor: Osman Bizim

Abstract:

In this work, a family of Somos 4 sequences is given and it is proved that all Somos 4 sequences associated to Tate normal forms with consist entirely of integers for . As an application, it is shown that there are infinitely many squares and infinitely many cubes in Somos 4 sequences associated to Tate normal forms. First chapter is the basis for the second chapter and the third chapter. Linear and bilinear recurrence sequences are discussed in this chapter. Also elliptic curves are considered in this chapter. In the second chapter, elliptic divisibility sequences are examined. Third chapter is the main part of the work. First, Somos sequences are defined. Then by obtaining the general terms of Somos 4 sequences associated to Tate normal forms, it is proved that these sequences with consist entirely of integers for . Finally, as an application, square terms and cube terms of these sequences are determined by using general terms.