On the Diophantine equation ((c+1)m2+1)x + (cm2-1)y = (am)z

Miyazaki, Takafumi

Publication:
On the Diophantine equation ((c+1)m2+1)x + (cm2-1)y = (am)z

dc.contributor.author	Miyazaki, Takafumi
dc.contributor.buuauthor	Kızıldere, Elif
dc.contributor.buuauthor	Soydan, Gökhan
dc.contributor.department	Fen Edebiyat Fakültesi
dc.contributor.department	Matematik Bölümü
dc.contributor.orcid	0000-0002-6321-4132
dc.contributor.orcid	0000-0002-7651-7001
dc.contributor.researcherid	M-9459-2017
dc.contributor.scopusid	57204173004
dc.contributor.scopusid	23566953200
dc.date.accessioned	2024-01-09T07:51:50Z
dc.date.available	2024-01-09T07:51:50Z
dc.date.issued	2018-08-10
dc.description.abstract	Suppose that c, in, and a are positive integers with a 11, 13 (mod 24) . In this work, we prove that when 2c + 1 = a(2), the Diophantine equation in the title has only solution (x, y, z) = (1,1,2) where m +/- 1 (mod a) and m > a(2) in positive integers. The main tools of the proofs are elementary methods and Baker's theory.
dc.identifier.citation	Kızıldere, E. vd. (2018). ''On the Diophantine equation ((c+1)m2+1)x + (cm2-1)y = (am)z''. Turkish Journal of Mathematics, 42(5), 2690-2698.
dc.identifier.endpage	2698
dc.identifier.issn	1300-0098
dc.identifier.issn	1303-6149
dc.identifier.issue	5
dc.identifier.scopus	2-s2.0-85054785989
dc.identifier.startpage	2690
dc.identifier.uri	https://doi.org/10.3906/mat-1803-14
dc.identifier.uri	https://journals.tubitak.gov.tr/math/vol42/iss5/45/
dc.identifier.uri	https://hdl.handle.net/11452/38884
dc.identifier.volume	42
dc.identifier.wos	000447946800046
dc.indexed.wos	SCIE
dc.language.iso	en
dc.publisher	Bilimsel ve Teknolojik Araştırma Kurumu
dc.relation.collaboration	Yurt dışı
dc.relation.journal	Turkish Journal of Mathematics
dc.relation.publicationcategory	Makale - Uluslararası Hakemli Dergi
dc.relation.tubitak	117F287
dc.relation.tubitak	16K17557
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	Mathematics
dc.subject	Exponential diophantine equation
dc.subject	Jacobi symbol
dc.subject	Lower bound for linear forms in logarithms
dc.subject	Linear-forms
dc.subject	2 logarithms
dc.subject	Conjecture
dc.subject.scopus	Diophantine Equation; Number; Linear Forms in Logarithms
dc.subject.wos	Mathematics
dc.title	On the Diophantine equation ((c+1)m2+1)x + (cm2-1)y = (am)z
dc.type	Article
dc.wos.quartile	Q3 (Mathematics)
dspace.entity.type	Publication
local.contributor.department	Fen Edebiyat Fakültesi/Matematik Bölümü
local.indexed.at	PubMed
local.indexed.at	Scopus