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RU-ALLRUSSIAN 1988 Problem 7

  • Answer

If rationals x, y satisfy x5+y5=2x2y2\mathbf{x}^{5} + \mathbf{y}^{5} = 2\mathbf{x}^{2}\mathbf{y}^{2} show that 1 - x y is the square of a rational.

Dataset text NuminaMath olympiads. Quoted with source.

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1 - xy = \left(\frac{1 - k^5}{1 + k^5}\right)^2

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