On the exponential Diophantine equation mx +(m+1) y =(1+m+m 2) z-Reference-Cited by-同舟云学术

On the exponential Diophantine equation mx +(m+1) y =(1+m+m 2) z

Published:2021-11-01 Issue:3 Volume:29 Page:23-32
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Alan Murat¹

Affiliation:

1. Yildiz Technical University , Department of Mathematics , Davutpasa Campus, 34210, Esenler , Istanbul , Turkey .

Abstract

Abstract Let m > 1 be a positive integer. We show that the exponential Diophantine equation mx + (m + 1) y = (1 + m + m 2) z has only the positive integer solution (x, y, z) = (2, 1, 1) when m ≥ 2.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/auom-2021-0032

Reference36 articles.

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2. [2] Alan, M. (2020) On the Exponential Diophantine Equation (m2 + m +1)x + my = (m + 1)z, Mediterr. J. Math., 17:189, 1-8.

3. [3] Bertók, C. (2016) The complete solution of the Diophantine equation (4m2 + 1)x + (5m2 − 1)y = (3m)z, Period Math Hung, 72, 37-42.10.1007/s10998-016-0111-x

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