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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/670175 |
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| _version_ | 1849412078474887168 |
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| author | Juanli Su Xiaoxue Li |
| author_facet | Juanli Su Xiaoxue Li |
| author_sort | Juanli Su |
| collection | DOAJ |
| 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). |
| format | Article |
| id | doaj-art-5eb5dddfd98f45748bbe07b98dfe2003 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5eb5dddfd98f45748bbe07b98dfe20032025-08-20T03:34:33ZengWileyAbstract 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 |
| spellingShingle | Juanli Su Xiaoxue Li The Exponential Diophantine Equation 4m2+1x+5m2-1y=(3m)z Abstract and Applied Analysis |
| title | 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_short | The Exponential Diophantine Equation 4m2+1x+5m2-1y=(3m)z |
| title_sort | exponential diophantine equation 4m2 1x 5m2 1y 3m z |
| url | http://dx.doi.org/10.1155/2014/670175 |
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