| 3N+1猜想中周期数存在的必要条件 |
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| 引用本文： | 李小纯. 3N+1猜想中周期数存在的必要条件[J]. 华中科技大学学报(自然科学版), 2005, 33(11): 102-103,107 |
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| 作者姓名： | 李小纯 |
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| 作者单位： | 空军雷达学院,指挥系,湖北,武汉,430019 |
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| 摘 要： | 给出了3N＋1猜想中周期为l的周期数的概念、数论函数potpn的定义以及二进制中的横和数的定义：A（xi,2）,高斯函数[x];同时给出了数论函数potpn的性质和potpm!的计算公式,利用数论函数potpn提出了3N＋1猜想中周期数存在的一个必要条件,为进一步研究3N＋1猜想中周期问题提供参考.
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| 关 键 词： | 周期数 数论函数 高斯函数 |
| 文章编号： | 1671-4512（2005）11-0102-02 |
| 收稿时间： | 2004-11-15 |
| 修稿时间： | 2004-11-15 |
Necessary condition of periodic numbers in 3N + 1 conjecture |
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| Li Xiaochun. Necessary condition of periodic numbers in 3N + 1 conjecture[J]. JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE, 2005, 33(11): 102-103,107 |
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| Authors: | Li Xiaochun |
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| Abstract: | After the introduction of the conception of periodic numbers in 3N 1 conjecture,numerical theory function was defined,the definition of sum-line number in binary bit: described and the Gauss function given.At the same time,some properties of number theory function and calculation formula of were discussed.By the use of number theory function,a necessary condition of periodic numbers in 3N 1 conjecture was proposed.The presentation of this necessary condition could play a certain role in further solution to periodic numbers question in 3N 1 conjecture. |
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| Keywords: | periodic numbers number theory function Gauss function |
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