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  • March 2010
  • Article
  • Proceedings of the American Mathematical Society

Further Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions

By: Shaofang Hong and Scott Duke Kominers
  • Format:Print
  • | Pages:5
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Abstract

For relatively prime positive integers u_0 and r, we consider the arithmetic progression {u_k := u_0+k*r} (0 <= k <= n). Define L_n := lcm{u_0,u_1,...,u_n} and let a >= 2 be any integer. In this paper, we show that, for integers alpha,r >= a and n >= 2*alpha*r, we have L_n >= u_0*r^{alpha+a-2}*(r+1)^n. In particular, letting a = 2 yields an improvement to the best previous lower bound on L_n (obtained by Hong and Yang) for all but three choices of alpha,r >= 2.

Keywords

Mathematical Methods

Citation

Hong, Shaofang, and Scott Duke Kominers. "Further Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions." Proceedings of the American Mathematical Society 138, no. 3 (March 2010): 809–813.
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About The Author

Scott Duke Kominers

Entrepreneurial Management
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