Repdigits Base b as Difference of Two Fibonacci Numbers

Siar, Zafer; Erduvan, Fatih; Keskin, Refik

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dc.contributor.authors	Siar, Zafer; Erduvan, Fatih; Keskin, Refik
dc.date.accessioned	2023-01-24T12:08:40Z
dc.date.available	2023-01-24T12:08:40Z
dc.date.issued	2022
dc.identifier.issn	2096-9856
dc.identifier.uri	http://dx.doi.org/10.4208/jms.v55n1.22.07
dc.identifier.uri	https://hdl.handle.net/20.500.12619/99532
dc.description	Bu yayın 06.11.1981 tarihli ve 17506 sayılı Resmî Gazete’de yayımlanan 2547 sayılı Yükseköğretim Kanunu’nun 4/c, 12/c, 42/c ve 42/d maddelerine dayalı 12/12/2019 tarih, 543 sayılı ve 05 numaralı Üniversite Senato Kararı ile hazırlanan Sakarya Üniversitesi Açık Bilim ve Açık Akademik Arşiv Yönergesi gereğince telif haklarına uygun olan nüsha açık akademik arşiv sistemine açık erişim olarak yüklenmiştir.
dc.description.abstract	In this paper, we find all repdigits expressible as difference of two Fibonacci numbers in base b for 2 <= b <= 10. The largest repdigits in base b, which can be written as difference of two Fibonacci numbers are F-9 - F-4 = 34 - 3=31= (11111)(2), F-14 - F-7=377 - 13=364= (111111)(3), F-14 - F-7 =377 - 13 =364 = (222)(4), F-9 - F-4 = 34 - 3 =31 = (111)(5), F-11 - F-4 = 89 - 3=86= (222)(6), F-13 - F-5 = 233 - 5=228= (444)(7), F-10 - F-2 =55 -1 =54 = (66)(8), F-14 - F-7 = 377-13 =364 = (444)(9), and F-15 - F-10 = 610 - 55 = 555 = (555)(10). As a result, it is shown that the largest Fibonacci number which can be written as a sum of a repdigit and a Fibonacci number is F-15 = 610 = 555+55 = 555 +F-10.
dc.language	English
dc.language.iso	eng
dc.publisher	GLOBAL SCIENCE PRESS
dc.relation.isversionof	10.4208/jms.v55n1.22.07
dc.subject	Mathematics
dc.subject	Fibonacci numbers
dc.subject	repdigit
dc.subject	Diophantine equations
dc.subject	linear forms in logarithms
dc.title	Repdigits Base b as Difference of Two Fibonacci Numbers
dc.type	Article
dc.identifier.volume	55
dc.identifier.startpage	84
dc.identifier.endpage	94
dc.relation.journal	JOURNAL OF MATHEMATICAL STUDY
dc.identifier.issue	1
dc.identifier.doi	10.4208/jms.v55n1.22.07
dc.identifier.eissn	2617-8702
dc.contributor.author	Siar, Zafer
dc.contributor.author	Erduvan, Fatih
dc.contributor.author	Keskin, Refik
dc.relation.publicationcategory	Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rights.openaccessdesignations	Bronze