Publication:
Integers of a quadratic field with prescribed sum and product

dc.contributor.authorBremner, Andrew
dc.contributor.authorSoydan, Gökhan
dc.contributor.buuauthorSOYDAN, GÖKHAN
dc.contributor.departmentBursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü
dc.contributor.researcheridM-9459-2017
dc.date.accessioned2024-09-30T10:46:50Z
dc.date.available2024-09-30T10:46:50Z
dc.date.issued2023-03-01
dc.description.abstractFor given k, $ is an element of Z we study the Diophantine systemx + y + z = k, xyz =lfor x, y, z integers in a quadratic number field, which has a history in the literature. When $ = 1, we describe all such solutions; only for k = 5, 6, do there exist solutions in which none of x, y, z are rational. The principal theorem of the paper is that there are only finitely many quadratic number fields K where the system has solutions x, y, z in the ring of integers of K. To illustrate the theorem, we solve the above Diophantine system for (k, $) = (-5, 7). Finally, in the case $ = k, the system is solved completely in imaginary quadratic fields, and we give (conjecturally) all solutions when $ = k <= 100 for real quadratic fields.
dc.identifier.doi10.4064/cm9023-11-2022
dc.identifier.eissn1730-6302
dc.identifier.issn0010-1354
dc.identifier.issue1
dc.identifier.urihttps://doi.org/10.4064/cm9023-11-2022
dc.identifier.urihttps://hdl.handle.net/11452/45497
dc.identifier.volume173
dc.identifier.wos000942494600001
dc.identifier.woshttps://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/colloquium-mathematicum/all/173/1/115046/integers-of-a-quadratic-field-with-prescribed-sum-and-product
dc.indexed.wosWOS.SCI
dc.language.isoen
dc.publisherArs Polona-ruch
dc.relation.journalColloquium Mathematicum
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectXyz = x+y+z
dc.subjectUnit solutions
dc.subjectEquation
dc.subjectScience & technology
dc.subjectPhysical sciences
dc.subjectMathematics
dc.titleIntegers of a quadratic field with prescribed sum and product
dc.typeArticle
dspace.entity.typePublication
relation.isAuthorOfPublication356f7af9-3f0f-4c82-8733-d98627634647
relation.isAuthorOfPublication.latestForDiscovery356f7af9-3f0f-4c82-8733-d98627634647

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