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ISSN 1088-6826(e) ISSN 0002-9939(p)

Improvements of lower bounds for the least common multiple of finite arithmetic progressions

Author(s): Shaofang Hong; Yujuan Yang
Journal: Proc. Amer. Math. Soc. 136 (2008), 4111-4114.
MSC (2000): Primary 11A05
Posted: July 17, 2008
MathSciNet review: 2431021
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Abstract: Let $u_0, r, \alpha$ and be positive integers such that . Let for $1\leq k\leq n$ . We prove that $L_n :={\rm lcm}\{u_0, u_1,\cdots, u_n\}\geq u_ 0r^\alpha (r+1)^n$ if $n>r^\alpha$ . This improves the lower bound of obtained previously by Farhi, Hong and Feng.

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Additional Information:

Shaofang Hong
Affiliation: Mathematical College, Sichuan University, Chengdu 610064, People’s Republic of China
Email: s-f.hong@tom.com, hongsf02@yahoo.com, sfhong@scu.edu.cn

Yujuan Yang
Affiliation: Mathematical College, Sichuan University, Chengdu 610064, People’s Republic of China
Email: y.j.yang@tom.com

DOI: 10.1090/S0002-9939-08-09565-8
PII: S 0002-9939(08)09565-8
Keywords: Arithmetic progression, least common multiple, lower bound.
Received by editor(s): September 18, 2007
Posted: July 17, 2008
Additional Notes: The first author was supported in part by the Program for New Century Excellent Talents in University, Grant No. NCET-06-0785.
Communicated by: Wen-Ching Winnie Li
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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