[1]戴丽霞,穆慧超.算术级数子集的最小公倍数[J].南京师大学报(自然科学版),2014,37(02):19.
　Dai Lixia,Mu Huichao.The Least Common Multiple of Arithmetic Progressions[J].Journal of Nanjing Normal University(Natural Science Edition),2014,37(02):19.
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算术级数子集的最小公倍数()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第37卷
期数:
2014年02期
页码:
19
栏目:
数学
出版日期:
2014-06-30

文章信息/Info

Title:
The Least Common Multiple of Arithmetic Progressions
作者:
戴丽霞; 穆慧超
南京师范大学数学科学学院,江苏 南京 210023
Author(s):
Dai Lixia; Mu Huichao
School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China
关键词:
最小公倍数; 算术级数; 概率
Keywords:
the least common multiple; arithmetic progression; probability
分类号:
O156.4
文献标志码:
A
摘要:
运用概率的方法研究了算术级数U的子集的最小公倍数.证明了对任意的0<θ<1,对几乎所有长度为[nθ]的U的子集A,都有loglcm{a:a∈A}=(1-θ)nθlogn+o(nθ).
Abstract:
For a positive arithmetic progression U={u+d,u+2d,…,u+nd},(u,d)=1,we study the logarithm of the least common multiple of subsets of the set U.We show that for any 0<θ<1,loglcm{a:a∈A}=(1-θ)nθlogn+o(nθ) for almost all sets AU of size [nθ].

参考文献/References:

[1]Cilleruelo J,Rué J,Sarka P,et al.The least common multiple of positive integers[EB/OL].[2011-12-13].http://arXiv.org/math/arXiv:1112.3013.
[2]Bateman P.Alimit involving least common multiples[J].Amer Math Monthly,2002,109(4):393-394.
[3]Canfield E R,Erdos P,Pomerance C.On a problem of oppenheim concerning factorisatio numerorum[J].J Number Theory,1983,17(1):1-28.
[4]Cilleruelo J.The least common multiple of a quadratic sequence[J].Composito Mathematica,2011,147(4):1 129-1 150.

相似文献/References:

[1]方金辉.一类特殊的算术级数存在性[J].南京师大学报(自然科学版),2007,30(04):17.
　Fang Jinhui.Existence of a Class of Special Arithmetic Progressions[J].Journal of Nanjing Normal University(Natural Science Edition),2007,30(02):17.

备注/Memo

备注/Memo:
Received data:2014-01-03.
Foundation item:Supported by the National Natural Science Foundation of China(11271185).
Corresponding author:Dai Lixia,Ph.D,associated professor,majored in number theory.E-mail:lilidainjnu@163.com
更新日期/Last Update: 2014-06-30