Further improvements of lower bounds for the least common multiples of arithmetic progressions

@inproceedings{Hong2010FurtherIO,
title={Further improvements of lower bounds for the least common multiples of arithmetic progressions},
author={S. Hong and S. Kominers},
year={2010}
}

For relatively prime positive integers uo and r, we consider the arithmetic progression {u k := u 0 + kr} n k=0 . 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 α,r ≥ a and n > 2αr, we have L n > u 0 r α+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 α, r > 2.