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RU-ALLRUSSIAN 1962 Problem 4

    Prove that there are no integers a, b, c, d such that the polynomial ax3+bx2+cx+d\mathrm{ax^3 + bx^2 + cx + d} equals 1 at x=19\mathrm{x = 19} and 2 at x=62\mathrm{x = 62} .

    Dataset text NuminaMath olympiads. Quoted with source.

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