For a positive integer $k$, denote by $f(k)$ the number of positive integer $m$ such that the remainder of $km$ modulo $2019^3$ is greater than $m$. Find the amount of different numbers among $f(1), f(2), ..., f(2019^3)$.
Problem
Source: 2021 Saudi Arabia Training Lists p30 https://artofproblemsolving.com/community/c2758131_2021_saudi_arabia_training_tests
Tags: number theory, remainder