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RU-ALLRUSSIAN 1963 Problem 12

  • Answer

Find all real p, q, a, b such that we have (2x−1)20−(ax+b)20=(x2+px+q)10(2\mathrm{x} - 1)^{20} - (\mathrm{ax} + \mathrm{b})^{20} = (\mathrm{x}^{2} + \mathrm{px} + \mathrm{q})^{10} for all x.

Dataset text NuminaMath olympiads. Quoted with source.

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a = (2^{20} - 1)^{1 / 20}, b = - \frac{a}{2}, p = -1, q = \frac{1}{4}

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