Question 144
Given two integers $m, n$ greater than $1$, and integers $a_1 \lt a_2 \lt \cdots \lt a_m$, prove that there exists a set $T$ of integers with $|T| \le 1 + \frac{a_m - a_1}{2n + 1}$ such that each $a_i$ can be written as $a_i = t + s$ for some $t \in T$, and $s \in [-n, n]$. (Posed by Leng Gangsong)