Question 145
Find the smallest positive integer $n \ge 9$ satisfying that for any group of integers $a_1, a_2, \dots, a_n$, there always exist $a_{i_1}, a_{i_2}, \dots, a_{i_9}$ ($1 \le i_1 \lt i_2 \lt \dots \lt i_9 \le n$) and $b_i \in \{4, 7\}$ ($i = 1, 2, \dots, 9$) such that $b_1 a_{i_1} + b_2 a_{i_2} + \dots + b_9 a_{i_9}$ is a multiple of 9.