| 关于指数Diophantine方程（x^m-1）／（x-1）=y^5 |
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| 引用本文： | 林木元.关于指数Diophantine方程（x^m-1）／（x-1）=y^5[J].湛江师范学院学报,2008,29(3):3-4. |
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| 作者姓名： | 林木元 |
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| 作者单位： | 贺州学院数学系,广西,贺州,542800 |
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| 摘 要： | 该文证明了：方程（x^m-1）／（x-1）=y^2．x〉1。y〉1，m〉2，没有正整数解（x，y，m）可使m=4（mod5）且m是平方数．
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| 关 键 词： | 指数Diophantine方程 分圆多项式 五次方幂 |
On the Exponential Diophantine Equation (xm-1)/(x-1)=y5 |
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| LIN Mu-yuan.On the Exponential Diophantine Equation (xm-1)/(x-1)=y5[J].Journal of Zhanjiang Normal College,2008,29(3):3-4. |
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| Authors: | LIN Mu-yuan |
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| Institution: | LIN Mu-yuan (Dept. of Math. , Hezhou College,Hezhou, Guangxi 542800, China) |
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| Abstract: | In this paper, we prove that the equation （x^m-1）/（x-1）=y^2 , x〉1, y〉1, m〉2, has no positive integer solution （x, y, m） with m as a square number and m=4（mod 5）. |
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| Keywords: | exponential diophantine equation eyelotomie polynomial quintic power |
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