MathNet 2009-part-04 — 175 problems (EN–VI) Question 99

If $1 \lt k_1 \lt k_2 \lt \dots \lt k_n$ and $a_1, a_2, \dots, a_n$ are integers such that for every integer $N$, $k_i \mid N - a_i$ for some $1 \le i \le n$, find the smallest possible value of $n$.