Publication:
The cubic congruence x(3)+ax(2)+bx+c equivalent to 0(mod p) and binary quadratic forms F(x, y) = ax(2)+bxy+cy(2)

dc.contributor.buuauthorTekcan, Ahmet
dc.contributor.departmentUludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü
dc.contributor.researcheridAAH-8518-2021
dc.contributor.scopusid55883777900
dc.date.accessioned2024-05-29T07:22:39Z
dc.date.available2024-05-29T07:22:39Z
dc.date.issued2007-10
dc.description.abstractLet F(x,y) ax(2) + bxy + cy(2) be a binary quadratic form of discriminant Delta = b(2) - 4ac for a, b, c is an element of Z, let p be a prime number and let F-p be a finite field. In this paper we formulate the number of integer solutions of cubic congruence x(3) + ax(2) + bx + c equivalent to 0 (mod p) over Fp for two specific binary quadratic forms F-1(k) (x, y) = x(2) + kxy + ky(2) and F-2(k) (x, y) = kx(2) + kxy + k(2) y(2) for integer k such that 1 <= k <= 9. Later we consider representation of primes by F-1(k) and F-2(k).
dc.identifier.endpage269
dc.identifier.issn0381-7032
dc.identifier.scopus2-s2.0-37049035341
dc.identifier.startpage257
dc.identifier.urihttps://hdl.handle.net/11452/41546
dc.identifier.volume85
dc.identifier.wos000250733900022
dc.indexed.pubmed
dc.indexed.scopusScopus
dc.indexed.wosSCIE
dc.language.isoen
dc.publisherCharles Babbage Research Centre
dc.relation.journalArs Combinatoria
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectBinary quadratic form
dc.subjectCubic congruence
dc.subjectRepresentation of primes by binary quadratic forms
dc.subjectCubic residue
dc.subjectMathematics
dc.subject.scopusReal Quadratic Fields; Pell's Equation; Continued Fraction
dc.subject.wosMathematics
dc.titleThe cubic congruence x(3)+ax(2)+bx+c equivalent to 0(mod p) and binary quadratic forms F(x, y) = ax(2)+bxy+cy(2)
dc.typeArticle
dspace.entity.typePublication
local.indexed.atWOS

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