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UA-UMO 2021 Problem 111

    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 ?

    Dataset text AI-MO AoPS. Quoted with source.

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