On the Diophantine equation (x+1)(k) + (x+2)(k) + ... + (2x)(k) = y(n)
| dc.contributor.author | Bérczes, Attila | |
| dc.contributor.author | Pink, István | |
| dc.contributor.buuauthor | Savaş, Gamze | |
| dc.contributor.buuauthor | Soydan, Gökhan | |
| dc.contributor.department | Uludağ Üniversitesi/Fen-Edebiyet Fakültesi/Matematik Bölümü. | tr_TR |
| dc.contributor.researcherid | FWV-5620-2022 | tr_TR |
| dc.contributor.researcherid | GEK-9891-2022 | tr_TR |
| dc.contributor.scopusid | 57206274023 | tr_TR |
| dc.contributor.scopusid | 23566953200 | tr_TR |
| dc.date.accessioned | 2023-09-24T12:54:13Z | |
| dc.date.available | 2023-09-24T12:54:13Z | |
| dc.date.issued | 2017-07-12 | |
| dc.description.abstract | In this work, we give upper bounds for n on the title equation. Our results depend on assertions describing the precise exponents of 2 and 3 appearing in the prime factorization of T-k(x) = (x + 1)(k) + (x + 2)(k) + ... + (2x)(k). Further, on combining Baker's method with the explicit solution of polynomial exponential congruences (see e.g. [6]), we show that for 2 <= x <= 13, k >= 1,y >= 2 and n >= 3 the title equation has no solutions. | en_US |
| dc.description.sponsorship | European Social Fund (ESF) - EFOP-3.6.1-16-2016-00022 | en_US |
| dc.description.sponsorship | European Union (EU) | en_US |
| dc.description.sponsorship | Austrian Science Fund (FWF) - P 24801-N26 | en_US |
| dc.description.sponsorship | Hungarian Academy of Sciences - 2014/70 | en_US |
| dc.description.sponsorship | Orszagos Tudomanyos Kutatasi Alapprogramok (OTKA) - K115479 - NK104208 | en_US |
| dc.identifier.citation | Berczes, A. vd. (2018). ''On the Diophantine equation (x+1)(k) + (x+2)(k) + ... + (2x)(k) = y(n)''. Journal of Number Theory, 183, 326-351. | en_US |
| dc.identifier.endpage | 351 | tr_TR |
| dc.identifier.issn | 0022-314X | |
| dc.identifier.issn | 1096-1658 | |
| dc.identifier.scopus | 2-s2.0-85029553067 | tr_TR |
| dc.identifier.startpage | 326 | tr_TR |
| dc.identifier.uri | https://doi.org/10.1016/j.jnt.2017.07.020 | |
| dc.identifier.uri | https://www.sciencedirect.com/science/article/pii/S0022314X17302895 | |
| dc.identifier.uri | http://hdl.handle.net/11452/33996 | |
| dc.identifier.volume | 183 | tr_TR |
| dc.identifier.wos | 000414380200016 | |
| dc.indexed.scopus | Scopus | en_US |
| dc.indexed.wos | SCIE | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Elsevier | en_US |
| dc.relation.bap | 2015-23 | tr_TR |
| dc.relation.collaboration | Yurt dışı | tr_TR |
| dc.relation.journal | Journal of Number Theory | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi | tr_TR |
| dc.relation.tubitak | BIDEB-2219 | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Mathematics | en_US |
| dc.subject | Power sums | en_US |
| dc.subject | Powers | en_US |
| dc.subject | Polynomial-exponential congruences | en_US |
| dc.subject | Linear forms in two logarithms | en_US |
| dc.subject | Sums | en_US |
| dc.subject.scopus | Diophantine Equation; Number; Linear Forms in Logarithms | en_US |
| dc.subject.wos | Mathematics | en_US |
| dc.title | On the Diophantine equation (x+1)(k) + (x+2)(k) + ... + (2x)(k) = y(n) | en_US |
| dc.type | Article | |
| dc.wos.quartile | Q3 | en_US |