Browsing by Author "Keskin, Refik"

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On the Lucas Sequence Equations V-n = kV(m) and U-n = kU(m)

Keskin, Refik; Şiar, Zafer (Institute of Mathematics, Polish Academy of Sciences, 2013)

Let P and Q be nonzero integers. The sequences of generalized Fibonacci and Lucas numbers are defined by U0=0, U1=1 and Un+1=PUn-QUn-1 for n≥1, and V0=2, V1=P and Vn+1=PVn-QVn-1 for n≥1, respectively. In this paper, we ...
Some New Identities Concerning Generalized Fibonacci and Lucas Numbers

Şiar, Zafer; Keskin, Refik (Hacettepe Üniversitesi, 2013)

In this paper we obtain some identities containing generalized Fibonacci and Lucas numbers. Some of them are new and some are well known. By using some of these identities we give some congruences concerning generalized ...
The Square Terms in Generalized Lucas Sequences

Şiar, Zafer; Keskin, Refik (Wiley, 2014)

Let P and Q be non-zero integers. The generalized Fibonacci sequence {U-n} and Lucas sequence {V-n} are defined by U-0 = 0, U-1 = 1 and Un+1 = PUn + QU(n-1) for n >= 1 and V-0 = 2, V-1 = P and Vn+1 = PVn + QV(n-1) for n ...