Question 148
An infinite strictly increasing sequence of positive integers $\{a_n\}_{n\ge 1}$ is given. It is also given that $a_n \le n + 2020$ and $n^3 a_n - 1$ is divisible by $a_{n+1}$ for any positive integer $n$. Prove that $a_n = n$ for any positive integer $n$. (Kanat Satylkhanov)