| 奇素数幂中的优美指数猜想 |
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| 引用本文： | 张作政,周斌彬.奇素数幂中的优美指数猜想[J].数学学习,2011(4):15-16. |
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| 作者姓名： | 张作政 周斌彬 |
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| 作者单位： | [1]长沙学院信息与计算科学系,湖南长沙410003 [2]湖南涉外经济学院计算机学部,湖南长沙410205 |
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| 基金项目： | 湖南省教育厅一般资助项目（10C0410）;长沙市科技计划项目（K0902210-11）;长沙学院人才引进项目（SF0904）. |
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| 摘 要： | 对于不小于7素数p,设1≤k≤p-1,则使用同余方法可证明方程n=pkp-1d（n）无正整数解,从而pkp-1不是优美指数,进而可以肯定＂存在无穷多个正整数不是优美指数＂.
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| 关 键 词： | 除数函数 优美指数 猜想 |
Indexes of Beauty among Power of Odd Primes |
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| ZHANG Zuo-zheng,ZHOU Bin-bin.Indexes of Beauty among Power of Odd Primes[J].Studies In College Mathematics,2011(4):15-16. |
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| Authors: | ZHANG Zuo-zheng ZHOU Bin-bin |
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| Institution: | 1. Department of Information and Computer Science, Changsha University, Changsha 410003, PRC; 2. School of Computer Science and Technology, Hunan International Economics University, Changsha 410205, PRC) |
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| Abstract: | Using the congruence method, the power of odd prime of the form p^kp-1 （p≥7,1≤ k ≤p-1） is proved not to be an index of beauty. This confirms the conjecture that there are infinitely many positive integers which are not indexes of beauty. |
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| Keywords: | divisor function index of beauty conjecture |
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