奇合数n不是完全数的一些命题 |
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引用本文: | 张四保. 奇合数n不是完全数的一些命题[J]. 安徽大学学报(自然科学版), 2016, 0(3): 6-11. DOI: 10.3969/j.issn.1000-2162.2016.03.002 |
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作者姓名: | 张四保 |
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作者单位: | 喀什大学数学与统计学院,新疆喀什,844008 |
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基金项目: | 国家自然科学基金资助项目(11201411);喀什大学科研基金资助项目(142513) |
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摘 要: | 奇完全数问题是数论中的一著名难题.探讨形如4 m+1的奇正整数n=παq2β11 q2β22…q2βss是否为完全数问题,给出其在σ(πα)≡2(mod8)条件下不是完全数的一些命题,由此可以类似地讨论其在σ(πα)≡6(mod8)条件下的情形,从而可以给出4 m+1型合数不是完全数的一系列条件.
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关 键 词: | 完全数 奇完全数 条件 |
Several results on the positive odd numbers n is not perfect number |
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Abstract: | The problem of perfect number was a well‐known difficult problem in number theory .In this paper ,the problem that the positive odd numbers of the form 4m+1 was not perfect number was studied .And in the condition ofσ(πα) ≡ 2(mod8) ,some results on the composite number n = παq2β11 …q2βss be the form of 4m + 1 was not perfect were given . Similarly ,the conditions of n = παq2β11 …q2βss was not odd perfect number in the condition ofσ(πα) ≡ 6(mod8) can be discussed .Therefore ,a series of conditions of the form of 4m+1 was not perfect number could be given . |
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Keywords: | perfect number odd perfect number condition |
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