Note on the Lower Bound of Least Common Multiple

作者：Oon Shea Ming^*

来源：Abstract and Applied Analysis, 2013, 2013: 218125.

DOI：10.1155/2013/218125

Consider a sequence of positive integers in arithmetic progression u(k) = u(0) + kr with (u(0), r) = 1. Denote the least common multiple of u(0), ... ,u(n) by L-n. We show that if n %26gt;= r(2) + r, then L-n %26gt;= u(0)r(r+1) (r + 1), and we obtain optimum result on.. in some cases for such estimate. Besides, for quadratic sequences m(2) + c, (m + 1)(2) + c, ... ,n(2) + c, we also show that the least common multiple is at least 2(n) when m %26lt;= [n/2], which sharpens a recent result of Farhi.

• 出版日期2013