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

Hong, Shaofang; Yang, Yujuan

doi:10.1090/S0002-9939-08-09565-8

Improvements of lower bounds for the least common multiple of finite arithmetic progressions
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by Shaofang Hong and Yujuan Yang

Proc. Amer. Math. Soc. 136 (2008), 4111-4114

DOI: https://doi.org/10.1090/S0002-9939-08-09565-8

Published electronically: July 17, 2008

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Abstract:

Let $u_0, r, \alpha$ and $n$ be positive integers such that $(u_ 0,r)=1$. Let $u_k=u_0+kr$ for $1\leq k\leq n$. We prove that $L_n :=\textrm {lcm}\{u_0, u_1,\cdots , u_n\}\geq u_ 0r^\alpha (r+1)^n$ if $n>r^\alpha$. This improves the lower bound of $L_n$ obtained previously by Farhi, Hong and Feng.

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