CWMO 2003 Problem 3

Let $n$ be a given positive integer. Find the smallest positive integer $u_n$ such that for any positive integer $d$ , in any $u_n$ consecutive odd positive integers, the number of them that can be divided by $d$ is not smaller than the number of odd integers among $1, 3, 5, \ldots, 2n - 1$ that can be divided by $d$ .