MathDB

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

Problem Statement