| 奇完全数存在条件及素因子个数 |
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| 引用本文： | 张四保,古丽扎尔&#;艾尼瓦尔.奇完全数存在条件及素因子个数[J].长春大学学报,2010,20(4):5-7,10. |
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| 作者姓名： | 张四保 古丽扎尔&#;艾尼瓦尔 |
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| 作者单位： | 喀什师范学院数学系,新疆喀什844007 |
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| 基金项目： | 喀什师范学院青年专项基金资助项目[092307] |
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| 摘 要： | 关于奇完全数的存在性问题是一个著名的数论难题，迄今远未解决。本文研究奇完全数的存在的条件，给出了奇完全数存在与否的一个充要条件，并且在奇完全数存在的条件下，给出了两类奇完全数的相异素因子的下界。
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| 关 键 词： | 完全数 奇完全数 约数和函数 |
The condition of existence and the numbers of prime divisors of odd perfect number |
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| Institution: | ZHANG Si-bao, Gulizhaer · ainiwaier ( Department of Mathematics, Kashgar Teachers College, Kashgar 844007, China) |
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| Abstract: | The existence of odd perfect numbers is a well-known number theoretic problem, which is under discussion. The existence condition of odd perfect number is studied, a necessary and sufficient condition of odd perfect number is given and the lower bound of distinct prime divisors of two kinds of odd perfect numbers is presented on the supposition that odd perfect number does exist. |
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| Keywords: | perfect number odd perfect number sum of divisors |
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