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On Concatenations of Fibonacci and Lucas Numbers

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dc.contributor.authorAlan, Murat
dc.date.accessioned2026-06-27T14:43:42Z
dc.date.issued2022
dc.description.abstractLet (F-n)(n >= 0) and (L-n)(n >= 0) be the Fibonacci and Lucas sequences. In this paper we determine all Fibonacci and Lucas numbers which are concatenations of two terms of the other sequence. This problem is identical to solve the Diophantine equations F-n = 10(d) L-m + L-k and L-n = 10(d) F-m + F-k in non-negative integers (n, m, k), where d denotes the number of digits of L-k and F-k, respectively. We use lower bounds for linear forms in logarithms and reduction method in Diophantine approximation to get the results.en
dc.description.urihttps://doi.org/10.1007/s41980-021-00668-7
dc.identifier.doi10.1007/s41980-021-00668-7
dc.identifier.eissn1735-8515
dc.identifier.endpage2741
dc.identifier.issn1017-060X
dc.identifier.issue5
dc.identifier.startpage2725
dc.identifier.urihttps://hdl.handle.net/20.500.14981/64018
dc.identifier.volume48
dc.identifier.wos000741906200001
dc.language.isoeng
dc.publisherSPRINGER SINGAPORE PTE LTD
dc.relation.ispartofBULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
dc.subjectFibonacci Numbers
dc.subjectLucas Numbers
dc.subjectDiophantine equations
dc.subjectLinear forms in logarithms
dc.subjectMathematics
dc.titleOn Concatenations of Fibonacci and Lucas Numbers
dc.typeArticle
dspace.entity.typePublication
local.import.sourceWOS

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