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The equation p(x) = 1/n has no rational roots

Source: International Zhautykov Olympiad 2013 - D2 - P1

January 17, 2013
quadraticsnumber theoryrelatively primealgebra unsolvedalgebra

Problem Statement

A quadratic trinomial p(x)p(x) with real coefficients is given. Prove that there is a positive integer nn such that the equation p(x)=1np(x) = \frac{1}{n} has no rational roots.
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