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Improvements of lower bounds for the least common multiple of finite arithmetic progressions
Authors:
Shaofang Hong and 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  and  be positive integers such that  . Let  for  . We prove that  if  . This improves the lower bound of  obtained previously by Farhi, Hong and Feng.
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- T. M. Apostol, Introduction to analytic number theory, Springer-Verlag, New York, 1976. MR 0434929 (55:7892)
- 2.
- G. Bachman and T. Kessler, On divisibility properties of certain multinomial coefficients. II, J. Number Theory 106 (2004), 1-12. MR 2029778 (2005a:11019)
- 3.
- B. Farhi, Minorations non triviales du plus petit commun multiple de certaines suites finies d'entiers, C.R. Acad. Sci. Paris, Ser. I 341 (2005), 469-474. MR 2180812 (2006g:11006)
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- B. Farhi, Nontrivial lower bounds for the least common multiple of some finite sequences of integers, J. Number Theory 125 (2007), 393-411. MR 2332595
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- B. Green and T. Tao, The primes contain arbitrarily long arithmetic progressions, Ann. of Math. (2) 167 (2008), 481-548.
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- 12.
- M. Nair, On Chebyshev-type inequalities for primes, Amer. Math. Monthly 89 (1982), 126-129. MR 643279 (83f:10043)
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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:
http://dx.doi.org/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
Article copyright:
© Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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