The Exponential Diophantine Equation 4m2+1x+5m2-1y=(3m)z

The Exponential Diophantine Equation 4m2+1x+5m2-1y=(3m)z

Let m be a positive integer. In this paper, using some properties of exponential diophantine equations and some results on the existence of primitive divisors of Lucas numbers, we prove that if m>90 and 3|m, then the equation 4m2+1x + 5m2-1y=(3m)z has only the positive integer solution (x,y,z)=(1...

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Main Authors: Juanli Su, Xiaoxue Li
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/670175
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spelling doaj-5eb5dddfd98f45748bbe07b98dfe20032020-11-24T23:41:44ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/670175670175The Exponential Diophantine Equation 4m2+1x+5m2-1y=(3m)zJuanli Su0Xiaoxue Li1School of Arts and Sciences, Yangling Vocational and Technical College, Yangling, Shaanxi 712100, ChinaSchool of Mathematics, Northwest University, Xi'an, Shaanxi 710127, ChinaLet m be a positive integer. In this paper, using some properties of exponential diophantine equations and some results on the existence of primitive divisors of Lucas numbers, we prove that if m>90 and 3|m, then the equation 4m2+1x + 5m2-1y=(3m)z has only the positive integer solution (x,y,z)=(1,1,2).http://dx.doi.org/10.1155/2014/670175
collection DOAJ
language English
format Article
sources DOAJ
author Juanli Su
Xiaoxue Li
spellingShingle Juanli Su
Xiaoxue Li
The Exponential Diophantine Equation 4m2+1x+5m2-1y=(3m)z
Abstract and Applied Analysis
author_facet Juanli Su
Xiaoxue Li
author_sort Juanli Su
title The Exponential Diophantine Equation 4m2+1x+5m2-1y=(3m)z
title_short The Exponential Diophantine Equation 4m2+1x+5m2-1y=(3m)z
title_full The Exponential Diophantine Equation 4m2+1x+5m2-1y=(3m)z
title_fullStr The Exponential Diophantine Equation 4m2+1x+5m2-1y=(3m)z
title_full_unstemmed The Exponential Diophantine Equation 4m2+1x+5m2-1y=(3m)z
title_sort exponential diophantine equation 4m2+1x+5m2-1y=(3m)z
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description Let m be a positive integer. In this paper, using some properties of exponential diophantine equations and some results on the existence of primitive divisors of Lucas numbers, we prove that if m>90 and 3|m, then the equation 4m2+1x + 5m2-1y=(3m)z has only the positive integer solution (x,y,z)=(1,1,2).
url http://dx.doi.org/10.1155/2014/670175
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AT xiaoxueli exponentialdiophantineequation4m21x5m21y3mz
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