Title

One Parameter Generalizations Of The Fibonacci And Lucas Numbersmourad

Abstract

We give one parameter generalizations of the Fibonacci and Lucas numbers denoted by {Fn(ø)} and {Ln(Ø)}, respectively. We evaluate the Hankel determinants with entries {1/F j+k+1{ø) :≤i,j≤ and {l/Lj+k+i(ø) :0≤ n}. We also find the entries in the inverse of {l/F j+k+1(ø) : 0 ≤i,j≤ n} and show that all its entries are integers. Some of the identities satisfied by the Fibonacci and Lucas numbers are extended to more general numbers. All integer solutions to three Diophantine equations related to the Pell equation are also found.

Publication Date

12-1-2008

Publication Title

Fibonacci Quarterly

Volume

46-47

Issue

2

Number of Pages

167-180

Document Type

Article

Personal Identifier

scopus

Socpus ID

69549126092 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/69549126092

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