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The Least Common Multiple of Arithmetic Progressions(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2014年02期
Page:
19-
Research Field:
数学
Publishing date:

Info

Title:
The Least Common Multiple of Arithmetic Progressions
Author(s):
Dai Lixia; Mu Huichao
School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China
Keywords:
the least common multiple; arithmetic progression; probability
PACS:
O156.4
DOI:
-
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].

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.

Memo

Memo:
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Last Update: 2014-06-30