Perfect squares in the sum and difference of balancing-like numbers

Sahukar, M. K.; Siar, Zafer; Keskin, Refik; Panda, G. K.

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dc.contributor.authors	Sahukar, M. K.; Siar, Zafer; Keskin, Refik; Panda, G. K.
dc.date.accessioned	2023-01-24T12:08:47Z
dc.date.available	2023-01-24T12:08:47Z
dc.date.issued	2022
dc.identifier.issn	1310-5132
dc.identifier.uri	http://dx.doi.org/10.7546/nntdm.2022.28.2.286-301
dc.identifier.uri	https://hdl.handle.net/20.500.12619/99627
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 study, we deal with the existence of perfect powers which are the sum and difference of two balancing numbers. Moreover, as a generalization we explore the perfect squares which are the sum and difference of two balancing-like numbers, where balancing-like sequence is defined recursively as G(n+1) = AG(n)-G(n-1) with initial terms G(0) = 0, G(1) = 1 for A >= 3.
dc.language	English
dc.language.iso	eng
dc.publisher	BULGARIAN ACAD SCIENCE
dc.relation.isversionof	10.7546/nntdm.2022.28.2.286-301
dc.subject	Mathematics
dc.subject	Balancing sequence
dc.subject	Balancing-like sequence
dc.subject	Pell sequence
dc.subject	Pell-like sequence
dc.subject	Diophantine equation
dc.title	Perfect squares in the sum and difference of balancing-like numbers
dc.type	Article
dc.identifier.volume	28
dc.identifier.startpage	286
dc.identifier.endpage	301
dc.relation.journal	NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
dc.identifier.issue	2
dc.identifier.doi	10.7546/nntdm.2022.28.2.286-301
dc.identifier.eissn	2367-8275
dc.contributor.author	Sahukar, M. K.
dc.contributor.author	Siar, Zafer
dc.contributor.author	Keskin, Refik
dc.contributor.author	Panda, G. K.
dc.relation.publicationcategory	Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rights.openaccessdesignations	gold