Further Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions
Abstract
For relatively prime positive integers u0 and r, we consider the arithmetic progression uk := u0+k*r (0 <= k <= n). Define Ln := lcmu0,u1,...,un 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 Ln >= u0*ralpha+a-2*(r+1)n. In particular, letting a = 2 yields an improvement to the best previous lower bound on Ln (obtained by Hong and Yang) for all but three choices of alpha,r >= 2.
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