| 关于连续正整数Diophantine方程的正整数解 |
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| 引用本文： | 邹兆南.关于连续正整数Diophantine方程的正整数解[J].重庆交通大学学报(自然科学版),2008,27(6):1168-1172. |
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| 作者姓名： | 邹兆南 |
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| 作者单位： | 重庆交通大学,理学院,重庆,400074 |
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| 摘 要： | 连续正整数Diophantine方程xn+(x+1)n+…+(x+h)n=(x+h+1)n的正整数解问题,是一个迄今为止尚未彻底解决的数论难题。目前已知的结果是:①当6≤n≤33时;②当n>3且为奇数时;③当34≤n≤200且为偶数时,该方程均无正整数解。采用多种素数模筛法证明了:当200
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| 关 键 词： | 连续整数 Diophantine方程 素数模 筛法 整数解 |
Positive Integral Solutions of Diophantine Equation of Continuous Positive Integers |
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| ZOU Zhao-nan.Positive Integral Solutions of Diophantine Equation of Continuous Positive Integers[J].Journal of Chongqing Jiaotong University,2008,27(6):1168-1172. |
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| Authors: | ZOU Zhao-nan |
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| Institution: | ZOU Zhao-nan(School of Science,Chongqing Jiaotong University,Chongqing 400074,China) |
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| Abstract: | The positive integral solutions of the Diophantine equation of continuous positive integers xn+(x+1)n+…+(x+h)n=(x+h+1)n are still unsettled until now.The latest result known at the present can be described as following: ①If 6≤n≤33;②If n>3 and n is an even integer;③If 34≤n≤200,the equation mentioned above has no positive integer solutions.Variety of sieve methods of prime modulus are adopted and it is proved that the Diophantine equation has no positive integer solutions when n is an even integer fitting with the condition 200
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| Keywords: | continuous integers Diophantine equations prime modulus sieve method integral solutions |
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