PL-OM 2011 Problem 6

Prove that it is impossible for polynomials $f_1(x),f_2(x),f_3(x),f_4(x)\in \mathbb{Q}[x]$ to satisfy $f_1^2(x)+f_2^2(x)+f_3^2(x)+f_4^2(x) = x^2+7.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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