Question 26
A positive integer $k$ is called *nice* if there exist positive integers $a_1, a_2, \dots, a_{2021}$ such that
(1) $a_i - a_j$ is not divisible by $2023$ for any pair $1 \le i \lt j \le 2021$,
(2) for any index $i$ there exists an index $j$ such that $a_i - k a_j$ is divisible by $2023$.
Find the largest nice number $k$ which is even and less than $100$.
(1) $a_i - a_j$ is not divisible by $2023$ for any pair $1 \le i \lt j \le 2021$,
(2) for any index $i$ there exists an index $j$ such that $a_i - k a_j$ is divisible by $2023$.
Find the largest nice number $k$ which is even and less than $100$.