FİBONACCİ POLİNOMLARININ VE P2 MERTEBEDEN BAZI HALKALARIN FİBONACCİ DİZİLERİNİN PERİYOTLARI

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Thesis Type: Doctorate

Institution Of The Thesis: Atatürk Üniversitesi, Fen Bilimleri Enstitüsü, Matematik Anabilim Dalı, Turkey

Approval Date: 2013

Thesis Language: Turkish

Student: YASEMİN TAŞYURDU

Principal Supervisor (For Co-Supervisor Theses): İnci GÜLTEKİN

Open Archive Collection: AVESIS Open Access Collection

Abstract:

In this study, we obtain the Fibonacci sequences of some rings of order p^2 by using recurrence F_(n+2)=A_1 F_(n+1)+A_0 F_n defined on the ring with identity, where F_0=0, the zero of the ring, F_1=1, the identity of the ring, n?0 and A_0, A_1 are arbitrary elements of the ring with identity of order p^2. It was shown that these sequences are periodic and their periods are obtained. It was shown that sequence obtained by reducing modulo m coefficient and exponent of each term of Fibonacci polynomials is periodic. It was seen that order of cylic group generated with Q=[?(x@1) ?(1@0)] matrix is equal to period of these sequences. Also, p is prime, Wall numbers of Fibonacci sequences according to modulo p are compared with the periods of sequences of Fibonacci polynomials and it was shown that this period always was even number.