Dilmen, Zülküf; Taşyurdu, Yasemin

In this study, { } Fibonacci sequence was defined over an arbitrary ring and its some properties are investigated.The terms of this sequence are derivated by Tridiagonal determinant of the matrix. It was shown that this sequence is periodic and their period is obtained. It was shown that the sequence obtained by reducing modulo coefficient and exponent of each Fibonacci sequence in arbitrary rings is periodic. It was seen that order of cyclic group generated with matrix = [] is equal to the period of this sequence where , are arbitrary elements of the ring. Also, the period of this sequence is compared with Wall number of Fibonacci sequence and it was shown that this period always was an even number

Çobanoğlu, Nurdan; Dilmen, Zülküf; Taşyurdu, Yasemin

Bu çalışmada, (Mikkawy ve Sogabe, 2010) çalışmasında tanımlanan yeni bir ailenin, { ( )} Fibonacci dizilerinin moduna göre basit periyodik diziler olduğu gösterildi. Yeni aile ve bilinen Fibonacci sayıları arasındaki bazı ilişkileri verdik. Ayrıca, yeni aile ve Lucas sayıları ile ilgili bazı teoremleri ispatladık