dc.contributor.authors | Siar, Z.; Keskin, R. | |
dc.date.accessioned | 2022-12-20T13:24:46Z | |
dc.date.available | 2022-12-20T13:24:46Z | |
dc.date.issued | 2022 | |
dc.identifier.issn | 0001-4346 | |
dc.identifier.uri | http://dx.doi.org/10.1134/S0001434622050248 | |
dc.identifier.uri | https://hdl.handle.net/20.500.12619/98991 | |
dc.description | Bu yayının lisans anlaşması koşulları tam metin açık erişimine izin vermemektedir. | |
dc.description.abstract | In this paper, we deal with the equation (a(n) - 2)(b(n) - 2) = x(2), 2 <= a < b, and a, b, x, n is an element of N. We solve this equation for (a, b) is an element of {(2, 10), (4, 100), (10, 58), (3, 45)}. Moreover, we show that (a(n) - 2)(b(n) - 2) = x(2) has no solution n, x if 2 vertical bar n and gcd(a, b) = 1. We also give a conjecture which says that the equation (2(n) - 2)((2P(k))(n) - 2) = x(2) has only the solution (n, x) = (2, Q(k)), where k > 3 is odd and P-k, Q(k) are the Pell and Pell Lucas numbers, respectively. We also conjecture that if the equation (a(n) - 2)(b(n) - 2) = x(2) has a solution n, x, then n <= 6. | |
dc.language | English | |
dc.language.iso | eng | |
dc.relation.isversionof | 10.1134/S0001434622050248 | |
dc.subject | Mathematics | |
dc.subject | Pell equation | |
dc.subject | exponential Diophantine equation | |
dc.subject | Lucas sequence | |
dc.title | On the Exponential Diophantine Equation (a(n)-2)(b(n)-2) = x(2)* | |
dc.identifier.volume | 111 | |
dc.identifier.startpage | 903 | |
dc.identifier.endpage | 912 | |
dc.relation.journal | MATHEMATICAL NOTES | |
dc.identifier.issue | 5-Jun | |
dc.identifier.doi | 10.1134/S0001434622050248 | |
dc.identifier.eissn | 1573-8876 | |
dc.contributor.author | Siar, Z. | |
dc.contributor.author | Keskin, R. | |
dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı |
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