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

Please use this identifier to cite or link to this item: http://hdl.handle.net/11452/29912

Title:	On the exponential diophantine equation (n-1)(x) + (n+2)(y) = n(z)
Authors:	Bai, Hairong Yuan, Pingzhi Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü. 0000-0002-6321-4132 Kızıldere, Elif Soydan, Gökhan 57204173004 23566953200
Keywords:	Exponential Diophantine equation Primitive divisors of Lucas sequences Jacobi symbol Lower bounds for linear forms in two logarithms Primitive divisors Linear-forms 2 Logarithms Conjecture Number Lucas Mathematics
Issue Date:	30-Mar-2020
Publisher:	Ars Polona-Ruch
Citation:	Bai, H. vd. (2020). "On the exponential diophantine equation (n-1)(x) + (n+2)(y) = n(z)". Colloquium Mathematicum, 161(2), 239-249.
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.
URI:	https://doi.org/10.4064/cm7668-6-2019 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 http://hdl.handle.net/11452/29912
ISSN:	0010-1354 1730-6302
Appears in Collections:	Scopus Web of Science

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