Question 92
Let $K$ and $N > K$ be fixed positive integers. Let $n$ be a positive integer and let $a_1, a_2, \dots, a_n$ be distinct integers. Suppose that whenever $m_1, m_2, \dots, m_n$ are integers, not all equal to $0$, such that $|m_i| \le K$ for each $i$, then the sum
$$
\sum_{i=1}^{n} m_i a_i
$$
is not divisible by $N$. What is the largest possible value of $n$?
$$
\sum_{i=1}^{n} m_i a_i
$$
is not divisible by $N$. What is the largest possible value of $n$?