Problem

Source: 2020 Korean MO winter camp Test 1 P6

Tags: number theory



Find all strictly increasing sequences $\{a_n\}_{n=0}^\infty$ of positive integers such that for all positive integers $k,m,n$ $$\frac{a_{n+1} +a_{n+2} +\dots +a_{n+k}}{k+m}$$is not an integer larger than $2020$.