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a_{2021}n^{2021}+a_{2020}n^{2020}+...+a_1n+a_0 divisible by 2021

Source: 2021 Ukraine NMO 11.1

April 2, 2021
number theory

Problem Statement

It is known that for some integers a2021,a2020,...,a1,a0a_{2021},a_{2020},...,a_1,a_0 the expression a2021n2021+a2020n2020+...+a1n+a0a_{2021}n^{2021}+a_{2020}n^{2020}+...+a_1n+a_0 is divisible by 20212021 for any arbitrary integer nn. Is it required that each of the numbers a2021,a2020,...,a1,a0a_{2021},a_{2020},...,a_1,a_0 also divisible by 20212021?
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