Divisibility of an F-L Type Convolution

Michael Wiemann and Curtis Cooper

A chapter in Applications of Fibonacci Numbers, 2004, pp 267-287 from Springer

Abstract: Abstract Sometimes when working on one problem, another problem and solution are found. The divisibility result in this paper is a consequence of attempts to prove some conjectures of Melham [9] related to the sum $$ {L_1}{L_3} \cdots {L_{2m + 1}}\sum\limits_{k = 1}^n {F_{2k}^{2m + 1}} , $$ where m is a nonnegative integer and n is a positive integer. Here, we use the usual notation for Fibonacci and Lucas numbers, i.e. $$ {F_0} = 0,{F_1} = 1,and\;{F_n} = {F_{n - 1}} + {F_{n - 2}}\quad for\;n \ge 2 $$ and $$ {L_0} = 2,{L_1} = 1,and\;{L_n} = {L_{n - 1}} + {L_{n - 2}}\quad for\;n \ge 2 $$ .

Keywords: 11B39 (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-306-48517-6_26

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DOI: 10.1007/978-0-306-48517-6_26

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