A note on the ternary purely exponential diophantine equation Ax + By = Cz with A + B = C2-Reference-Cited by-同舟云学术

A note on the ternary purely exponential diophantine equation Ax + By = Cz with A + B = C2

Published:2020-06 Issue:2 Volume:57 Page:200-206
ISSN:0081-6906
Container-title:Studia Scientiarum Mathematicarum Hungarica
language:
Short-container-title:Studia Scientiarum Mathematicarum Hungarica

Author:

kizildere Elif¹,le Maohua²,Soydan Gökhan³

Affiliation:

1. 1Department of Mathematics, Bursa Uludağ University, 16059 Bursa, Turkey

2. 2Institute of Mathematics, Lingnan Normal College, Zhanjiang, Guangdong, 524048 China

3. 3Department of Mathematics, Bursa Uludağ University, 16059 Bursa, Turkey

Abstract

AbstractLet l,m,r be fixed positive integers such that 2| l, 3lm, l > r and 3 | r. In this paper, using the BHV theorem on the existence of primitive divisors of Lehmer numbers, we prove that if min{rlm2 − 1,(l − r)lm2 + 1} > 30, then the equation (rlm2 − 1)x + ((l − r)lm2 + 1)y = (lm)z has only the positive integer solution (x,y,z) = (1,1,2).

Publisher

Akademiai Kiado Zrt.

Subject

General Mathematics

Link

https://akjournals.com/downloadpdf/journals/012/57/2/article-p200.xml

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