Publication: A note on the diophantine equation x2=4pn-4pm + l2
dc.contributor.author | Abu Muriefah, Fadwa S. | |
dc.contributor.author | Le, Maohua | |
dc.contributor.buuauthor | Soydan, Gokhan | |
dc.contributor.buuauthor | SOYDAN, GÖKHAN | |
dc.contributor.department | Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü. | |
dc.date.accessioned | 2024-07-01T06:50:55Z | |
dc.date.available | 2024-07-01T06:50:55Z | |
dc.date.issued | 2021-11-11 | |
dc.description.abstract | Let l be a fixed odd positive integer. In this paper, using some classical results on the generalized Ramanujan-Nagell equation, we completely derive all solutions (p, x, m, n) of the equation x(2) = 4p(n)-4p(m)+l(2) with l(2) < 4p(m) for any l > 1, where p is a prime, x, m, n are positive integers satisfying gcd(x, l) = 1 and m < n. Meanwhile we give a method to solve the equation with l(2) > 4p(m). As an example of using this method, we find all solutions (p, x, m, n) of the equation for l is an element of {5, 7}. | |
dc.identifier.doi | 10.1007/s13226-021-00197-3 | |
dc.identifier.endpage | 922 | |
dc.identifier.issn | 0019-5588 | |
dc.identifier.issue | 4 | |
dc.identifier.startpage | 915 | |
dc.identifier.uri | https://doi.org/10.1007/s13226-021-00197-3 | |
dc.identifier.uri | https://hdl.handle.net/11452/42622 | |
dc.identifier.volume | 53 | |
dc.identifier.wos | 000717393700001 | |
dc.indexed.wos | WOS.SCI | |
dc.language.iso | en | |
dc.publisher | Indian Nat Sci Acad | |
dc.relation.journal | Indian Journal Of Pure & Applied Mathematics | |
dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi | |
dc.rights | info:eu-repo/semantics/closedAccess | |
dc.subject | Polynomial-exponential diophantine equation | |
dc.subject | Generalized ramanujan-nagell equation | |
dc.subject | Baker's method | |
dc.subject | Science & technology | |
dc.subject | Physical sciences | |
dc.subject | Mathematics | |
dc.subject | Mathematics | |
dc.title | A note on the diophantine equation x2=4pn-4pm + l2 | |
dc.type | Article | |
dspace.entity.type | Publication | |
relation.isAuthorOfPublication | 356f7af9-3f0f-4c82-8733-d98627634647 | |
relation.isAuthorOfPublication.latestForDiscovery | 356f7af9-3f0f-4c82-8733-d98627634647 |