Publication: On the diophantine equation (5 pn 2 - 1) x
dc.contributor.author | Kızıldere, Elif | |
dc.contributor.author | Soydan, Gökhan | |
dc.contributor.buuauthor | SOYDAN, GÖKHAN | |
dc.contributor.buuauthor | Kızıldere, Elif | |
dc.contributor.department | Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü | |
dc.contributor.orcid | 0000-0002-6321-4132 | |
dc.contributor.researcherid | M-9459-2017 | |
dc.contributor.researcherid | GRN-4828-2022 | |
dc.date.accessioned | 2024-07-05T10:34:06Z | |
dc.date.available | 2024-07-05T10:34:06Z | |
dc.date.issued | 2020-03-01 | |
dc.description.abstract | Let p be a prime number with p > 3, p 3 (mod 4) and let n be a positive integer. In this paper, we prove that the Diophantine equation (5pn(2) - 1)(x) + (p(p - 5)n(2) + 1)(y) = (pn)(z) has only the positive integer solution (x; y; z) = (1; 1; 2) where pn +/- 1 (mod 5). As an another result, we show that the Diophantine equation (35n(2) - 1)(x) + (14n(2) + 1)(y) = (7n)(z) has only the positive integer solution (x, y, z) = (1; 1; 2) where n +/- 3 (mod 5) or 5 vertical bar n. On the proofs, we use the properties of Jacobi symbol and Baker's method. | |
dc.identifier.doi | 10.5831/HMJ.2020.42.1.139 | |
dc.identifier.eissn | 2288-6176 | |
dc.identifier.endpage | 150 | |
dc.identifier.issn | 1225-293X | |
dc.identifier.issue | 1 | |
dc.identifier.startpage | 139 | |
dc.identifier.uri | https://doi.org/10.5831/HMJ.2020.42.1.139 | |
dc.identifier.uri | http://koreascience.or.kr/article/JAKO202009444381938.page | |
dc.identifier.uri | https://hdl.handle.net/11452/42971 | |
dc.identifier.volume | 42 | |
dc.identifier.wos | 000523592000010 | |
dc.indexed.wos | WOS.ESCI | |
dc.language.iso | en | |
dc.publisher | Honam Mathematical Soc | |
dc.relation.journal | Honam Mathematical Journal | |
dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi | |
dc.relation.tubitak | 117F287 | |
dc.rights | info:eu-repo/semantics/closedAccess | |
dc.subject | Linear-forms | |
dc.subject | 2 logarithms | |
dc.subject | Conjecture | |
dc.subject | Exponential diophantine equation | |
dc.subject | Jacobi symbol | |
dc.subject | Baker's method | |
dc.subject | Science & technology | |
dc.subject | Physical sciences | |
dc.subject | Mathematics | |
dc.title | On the diophantine equation (5 pn 2 - 1) x | |
dc.type | Article | |
dspace.entity.type | Publication | |
relation.isAuthorOfPublication | 356f7af9-3f0f-4c82-8733-d98627634647 | |
relation.isAuthorOfPublication.latestForDiscovery | 356f7af9-3f0f-4c82-8733-d98627634647 |