[1]吴金钗.奇数的拆分循环及应用[J].华侨大学学报(自然科学版),2021,42(5):701-708.[doi:10.11830/ISSN.1000-5013.202103002]
　WU Jincai.Odd Number Splitting Cycle and Its Application[J].Journal of Huaqiao University(Natural Science),2021,42(5):701-708.[doi:10.11830/ISSN.1000-5013.202103002]
点击复制

奇数的拆分循环及应用()
分享到：

《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第42卷
期数:
2021年第5期
页码:
701-708
栏目:
出版日期:
2021-09-20

文章信息/Info

Title:
Odd Number Splitting Cycle and Its Application
文章编号:
1000-5013(2021)05-0701-08
作者:
吴金钗
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
WU Jincai
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
Mersenne数;  Fermat数;  奇数和式拆分与差式拆分;  素数的拆分循环
Keywords:
Mersenne numbers;  Fermat numbers;  odd number sum splitting and difference splitting;  prime number splitting cycle
分类号:
O156.1
DOI:
10.11830/ISSN.1000-5013.202103002
文献标志码:
A
摘要:
因Mersenne数(Mp)和Fermat数(Fn)都是二进制形式的数,故采用二进制数研究Mp,Fn的性质,导出奇数的拆分循环概念和相关理论.结果表明:这套理论可用于分析大数的性质及分解,并具有一定的普遍性和通用性.
Abstract:
Because both Mersenne numbers(Mp)and Fermat numbers(Fn)are numbers in binary form, binary numbers were used to study the properties of Mp, Fn. The concept of odd number splitting cycles and related theories are derived. The results show that these theories can be used to analyze the properties of large numbers and their decomposition, and possess a certain universality and versatility.

参考文献/References:

[1] 华罗庚.数论导引[M].北京:科学出版社,1957.
[2] WIKIPEDIA.Mersenne prime[EB/OL].(2017-07-21)[2021-02-05] .http://tcs.nju.edu.cn/wiki/index.php/Mersenne_prime.
[3] 蔡天新.完美数与黄金分割比[J].数学进展,2019,48(4):127-129.DOI:10.11845/sxjz.2019001e.
[4] 周忠奇,黄文豪.梅森数、瓦格斯塔夫数推广及其整数因子研究[J].佳木斯大学学报(自然科学版),2017,35(6):1009-1010.DOI:10.3969/j.issn.1008-1402.2017.06.034.
[5] 陈景润.初等数论Ⅰ[M].北京: 科学出版社,1978.
[6] 陈景润.初等数论Ⅱ[M].北京: 科学出版社,1980.
[7] 闵嗣鹤,严士健.初等数论[M].2版.北京: 人民教育出版社,1982.
[8] BANERJEE S,BATAVIA M,KANE B,et al.Fermat’s polygonal number theorem for repeated generalized polygonal numbers[J].Journal of Number Theory,2020,220:163-181.DOI:10.1016/j.jnt.2020.05.024.
[9] BANERJEE S,BATAVIA M,KANE B,et al.Expect at most one billionth of a new Fermat Prime![J].Mathematical Intelligencer,2016,39(1):1-3.DOI:10.1007/s00283-016-9644-3.
[10] CAMBRAIA A J,KNAPP M P,LEMOS A,et al.On prime factors of Mersenne numbers[EB/OL].(2021-04-29)[2021-05-03] .https://arxiv.org/pdf/1606.08690.pdf.
[11] KELLER W.Prime factors k·2n+1 of fermat numbers fm and complete factoring status[EB/OL].(2021-03-03)[2021-05-03] .http://www.prothsearch.com/fermat.html.
[12] KELLER W.Distributed search for fermat number divisors[EB/OL].(2020-10-22)[2021-02-05] .http://www.fermatsearch.org/.
[13] WANG Xinbo.Algorithm available for factoring big fermat numbers[J].Journal of Software,2020,15(3):86-97.DOI:10.17706/jsw.15.3.86-97.
[14] 王钰.一个费马数分解算法的剖析与优化[J].现代计算机,2020(36):64-67.DOI:10.3969/j.issn.1007-1423.2020.36.012.

备注/Memo

备注/Memo:
收稿日期: 2021-03-02
通信作者: 吴金钗(1938-),男,副教授,主要从事数论、偏微分方程的研究.E-mail:fruitful@xmu.edu.cn.
更新日期/Last Update: 2021-09-20