Note on the Lower Bound of Least Common Multiple

Shea-Ming Oon

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: Consider a sequence of positive integers in arithmetic progression uk = u0 + kr with (u0, r) = 1. Denote the least common multiple of u0, …, un by Ln. We show that if n⩾r2 + r, then Ln⩾u0rr+1(r + 1), and we obtain optimum result on n in some cases for such estimate. Besides, for quadratic sequences m2 + c, (m + 1)2 + c, …, n2 + c, we also show that the least common multiple is at least 2n when m ⩽ ⌈n/2⌉, which sharpens a recent result of Farhi.

Date: 2013
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https://doi.org/10.1155/2013/218125

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:218125

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