BG-MO 2021 Problem 4

Two infinite arithmetic sequences with positive integers are given: $$a_1<a_2<a_3<\cdots ; b_1<b_2<b_3<\cdots$$ It is known that there are infinitely many pairs of positive integers $(i,j)$ for which $i\leq j\leq i+2021$ and $a_i$ divides $b_j$ . Prove that for every positive integer $i$ there exists a positive integer $j$ such that $a_i$ divides $b_j$ .