On the reciprocal sum of the fourth power of Fibonacci numbers

Won Tae Hwang; Jong Do Park; Kyunghwan Song

doi:10.1515/math-2022-0525

On the reciprocal sum of the fourth power of Fibonacci numbers

Won Tae Hwang
, Jong Do Park^*
, Kyunghwan Song

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

2 Scopus citations

Abstract

Let fn be the nth Fibonacci number with f1 = f2 = 1. Recently, the exact values of ⌊(Σk=n∞ 1/fks)-1⌋ have been obtained only for s = 1, 2, where ⌊ x ⌋ is the floor function. It has been an open problem for s ≥ 3. In this article, we consider the case of s = 4 and show that 'Equation Presented', where {x} = x - ⌊ x ⌋.

Original language	English
Pages (from-to)	1642-1655
Number of pages	14
Journal	Open Mathematics
Volume	20
Issue number	1
DOIs	https://doi.org/10.1515/math-2022-0525
State	Published - 2022.01.1

Keywords

Catalan's identity
Fibonacci number
Lucas number
Pisano period
recurrence relation

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1515/math-2022-0525

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title = "On the reciprocal sum of the fourth power of Fibonacci numbers",

abstract = "Let fn be the nth Fibonacci number with f1 = f2 = 1. Recently, the exact values of ⌊(Σk=n∞ 1/fks)-1⌋ have been obtained only for s = 1, 2, where ⌊ x ⌋ is the floor function. It has been an open problem for s ≥ 3. In this article, we consider the case of s = 4 and show that 'Equation Presented', where \{x\} = x - ⌊ x ⌋.",

keywords = "Catalan's identity, Fibonacci number, Lucas number, Pisano period, recurrence relation",

author = "Hwang, \{Won Tae\} and Park, \{Jong Do\} and Kyunghwan Song",

note = "Publisher Copyright: {\textcopyright} 2022 the author(s).",

year = "2022",

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day = "1",

doi = "10.1515/math-2022-0525",

language = "English",

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TY - JOUR

T1 - On the reciprocal sum of the fourth power of Fibonacci numbers

AU - Hwang, Won Tae

AU - Park, Jong Do

AU - Song, Kyunghwan

PY - 2022/1/1

Y1 - 2022/1/1

N2 - Let fn be the nth Fibonacci number with f1 = f2 = 1. Recently, the exact values of ⌊(Σk=n∞ 1/fks)-1⌋ have been obtained only for s = 1, 2, where ⌊ x ⌋ is the floor function. It has been an open problem for s ≥ 3. In this article, we consider the case of s = 4 and show that 'Equation Presented', where {x} = x - ⌊ x ⌋.

AB - Let fn be the nth Fibonacci number with f1 = f2 = 1. Recently, the exact values of ⌊(Σk=n∞ 1/fks)-1⌋ have been obtained only for s = 1, 2, where ⌊ x ⌋ is the floor function. It has been an open problem for s ≥ 3. In this article, we consider the case of s = 4 and show that 'Equation Presented', where {x} = x - ⌊ x ⌋.

KW - Catalan's identity

KW - Fibonacci number

KW - Lucas number

KW - Pisano period

KW - recurrence relation

UR - https://www.scopus.com/pages/publications/85144503569

U2 - 10.1515/math-2022-0525

DO - 10.1515/math-2022-0525

M3 - Journal article

AN - SCOPUS:85144503569

SN - 2391-5455

VL - 20

SP - 1642

EP - 1655

JO - Open Mathematics

JF - Open Mathematics

IS - 1

ER -

On the reciprocal sum of the fourth power of Fibonacci numbers

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

Access to Document

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