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INMO 2024 Problem 3

    Let pp be an odd prime number and a,b,ca, b, c be integers so that the integers

    a2023+b2023,b2024+c2024,c2025+a2025a^{2023}+b^{2023}, b^{2024}+c^{2024}, c^{2025}+a^{2025}

    are all divisible by pp. Prove that pp divides each of a,ba, b, and cc.

    Dataset text NuminaMath olympiads. Quoted with source.

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