The Pell-Fibonacci Sequence Modulo m

Authors : Yeşim AKÜZÜM

Pages : 280-284

View : 46 | Download : 8

Publication Date : 2020-12-30

Article Type : Research Paper

Abstract :In [6], Deveci defined the Pell-Fibonacci sequence as follows: P − F insert ignore into journalissuearticles values(n + 4); = 3P − F insert ignore into journalissuearticles values(n + 3); − 3P − F insert ignore into journalissuearticles values(n + 1); − P − F insert ignore into journalissuearticles values(n); for n ≥ 0 with initial constants P − F insert ignore into journalissuearticles values(0); = P − F insert ignore into journalissuearticles values(1); = P − F insert ignore into journalissuearticles values(2); = 0,P − F insert ignore into journalissuearticles values(3); = 1. Also, he derived the permanental and determinantal representations of the Pell-Fibonacci numbers and he obtained miscellaneous properties of the Pell-Fibonacci numbers by the aid of the generating function and the generating matrix of the Pell-Fibonacci sequence. The linear recurrence sequences appear in modern research in many fields from mathematics, physics, computer, architecture to nature and art; see, for example, [2, 4, 13, 18]. In this paper, we obtain the cyclic groups which are produced by generating matrix of the Pell-Fibonacci sequence when read modulo m. Furthermore, we research the Pell-Fibonacci sequence modulo m, and then we derive the relationship between the order the cyclic groups obtained and the periods of the Pell-Fibonacci sequence modulo m.
Keywords : The Pell Fibonacci sequence, Modulo, Period

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