On the exponential diophantine equation (n-1)(x) + (n+2)(y) = n(z)

Bai, Hairong; Yuan, Pingzhi

Publication:
On the exponential diophantine equation (n-1)(x) + (n+2)(y) = n(z)

dc.contributor.author	Bai, Hairong
dc.contributor.author	Yuan, Pingzhi
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.scopusid	57204173004
dc.contributor.scopusid	23566953200
dc.date.accessioned	2022-12-15T11:09:33Z
dc.date.available	2022-12-15T11:09:33Z
dc.date.issued	2020-03-30
dc.description.abstract	Suppose that n is a positive integer. We show that the only positive integer solutions (n, x, y, z) of the exponential Diophantine equation (n - 1)(x) + (n + 2)(y) = nz, n >= 2, xyz not equal 0, are (3, 2, 1, 2), (3,1, 2, 3). The main tools in the proofs are Baker's theory and Bilu-Hanrot-Voutier's result on primitive divisors of Lucas numbers.
dc.description.sponsorship	National Natural Science Foundation of China (NSFC) (11671153)
dc.identifier.citation	Bai, H. vd. (2020). "On the exponential diophantine equation (n-1)(x) + (n+2)(y) = n(z)". Colloquium Mathematicum, 161(2), 239-249.
dc.identifier.endpage	249
dc.identifier.issn	0010-1354
dc.identifier.issn	1730-6302
dc.identifier.issue	2
dc.identifier.scopus	2-s2.0-85084753117
dc.identifier.startpage	239
dc.identifier.uri	https://doi.org/10.4064/cm7668-6-2019
dc.identifier.uri	https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/colloquium-mathematicum/all/161/2/113556/on-the-exponential-diophantine-equation-n-1-x-n-2-y-n-z
dc.identifier.uri	http://hdl.handle.net/11452/29912
dc.identifier.volume	161
dc.identifier.wos	000571757800005
dc.indexed.wos	SCIE
dc.language.iso	en
dc.publisher	Ars Polona-Ruch
dc.relation.collaboration	Yurt dışı
dc.relation.journal	Colloquium Mathematicum
dc.relation.publicationcategory	Makale - Uluslararası Hakemli Dergi
dc.relation.tubitak	117f287
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	Exponential Diophantine equation
dc.subject	Primitive divisors of Lucas sequences
dc.subject	Jacobi symbol
dc.subject	Lower bounds for linear forms in two logarithms
dc.subject	Primitive divisors
dc.subject	Linear-forms
dc.subject	2 Logarithms
dc.subject	Conjecture
dc.subject	Number
dc.subject	Lucas
dc.subject	Mathematics
dc.subject.scopus	Diophantine Equation; Number; Linear Forms in Logarithms
dc.subject.wos	Mathematics
dc.title	On the exponential diophantine equation (n-1)(x) + (n+2)(y) = n(z)
dc.type	Article
dc.wos.quartile	Q4
dspace.entity.type	Publication
local.contributor.department	Fen Edebiyat Fakültesi/Matematik Bölümü
local.indexed.at	Scopus
local.indexed.at	WOS