Problem

Source: Kosovo MO 2020 Grade 12, Problem 2

Tags: Kosovo, national olympiad, Olympiad, number theory, divisible



Let $a_1,a_2,...,a_n$ be integers such that $a_1^{20}+a_2^{20}+...+a_n^{20}$ is divisible by $2020$. Show that $a_1^{2020}+a_2^{2020}+...+a_n^{2020}$ is divisible by $2020$.