| 关于Diophantine方程(ax~4-1)/(ax-1)=y~n |
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| 作者单位： | 湛江师范学院数学系 广东湛江524048 |
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| 摘 要： | 设a是大于1的正整数,证明方程(ax4-1)/(ax-1)=yn仅当a=4时有正整数解(x,y,n)=(2,3,2)适合m in(x,y,n)>1.
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| 关 键 词： | 指数Diophantine方程 正整数解 存在性 |
On the Diophantine Equation(ax~4-1)/(ax-1)=y~n |
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| Authors: | LE Mao-hua |
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| Abstract: | Let a be a positive integer with a>1.In this paper,we prove that the equation(ax~4-1)/(ax-1)=y~n has no positive integer solutions(x,y,n) with min(x,y,n)>1,except when a=4 and(x,y,n)=(2,3,2). |
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| Keywords: | exponential diophantine equation positive integer solution existence |
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