About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 218125, 4 pages
http://dx.doi.org/10.1155/2013/218125
Research Article

Note on the Lower Bound of Least Common Multiple

Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia

Received 1 July 2012; Revised 24 December 2012; Accepted 10 January 2013

Academic Editor: Pekka Koskela

Copyright © 2013 Shea-Ming Oon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. Green and T. Tao, “The primes contain arbitrarily long arithmetic progressions,” Annals of Mathematics, vol. 167, no. 2, pp. 481–547, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. D. Hanson, “On the product of the primes,” Canadian Mathematical Bulletin. Bulletin Canadien de Mathématiques, vol. 15, pp. 33–37, 1972. View at Zentralblatt MATH · View at MathSciNet
  3. M. Nair, “On Chebyshev-type inequalities for primes,” The American Mathematical Monthly, vol. 89, no. 2, pp. 126–129, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. H. N. Shapiro, “On the number of primes less than or equal x,” Proceedings of the American Mathematical Society, vol. 1, pp. 346–348, 1950. View at Zentralblatt MATH · View at MathSciNet
  5. B. Farhi, “Minorations non triviales du plus petit commun multiple de certaines suites finies d'entiers,” Comptes Rendus Mathématique. Académie des Sciences. Paris, vol. 341, no. 8, pp. 469–474, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. B. Farhi and D. Kane, “New results on the least common multiple of consecutive integers,” Proceedings of the American Mathematical Society, vol. 137, no. 6, pp. 1933–1939, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. S. Hong and G. Qian, “The least common multiple of consecutive arithmetic progression terms,” Proceedings of the Edinburgh Mathematical Society, vol. 54, no. 2, pp. 431–441, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  8. S. Hong and Y. Yang, “Improvements of lower bounds for the least common multiple of finite arithmetic progressions,” Proceedings of the American Mathematical Society, vol. 136, no. 12, pp. 4111–4114, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. Hong and S. D. Kominers, “Further improvements of lower bounds for the least common multiples of arithmetic progressions,” Proceedings of the American Mathematical Society, vol. 138, no. 3, pp. 809–813, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. R. Wu, Q. Tan, and S. Hong, “New lower bounds for the least common multiple of arithmetic progressions,” Chinese Annals of Mathematics. In press.
  11. B. Farhi, “Nontrivial lower bounds for the least common multiple of some finite sequences of integers,” Journal of Number Theory, vol. 125, no. 2, pp. 393–411, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. G. Qian, Q. Tan, and S. Hong, “The least common multiple of consecutive terms in a quadratic progression,” Bulletin of the Australian Mathematical Society, vol. 86, pp. 389–404, 2012.
  13. S. Hong and W. Feng, “Lower bounds for the least common multiple of finite arithmetic progressions,” Comptes Rendus Mathématique. Académie des Sciences. Paris, vol. 343, no. 11-12, pp. 695–698, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet