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RU-ALLRUSSIAN 1986 Problem 1

  • Answer

The quadratic x2+ax+b+1\mathbf{x}^{2} + \mathbf{ax} + \mathbf{b} + 1 has roots which are positive integers. Show that (a2+b2)(\mathbf{a}^{2} + \mathbf{b}^{2}) is composite.

Dataset text NuminaMath olympiads. Quoted with source.

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a^2 + b^2 = (c^2 + 1)(d^2 + 1)

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