ÖMO 1997 Problem 4

Determine all quadruples $(a,b,c,d)$ of real numbers satisfying the equation:

$256a^3 b^3 c^3 d^3=(a^6+b^2+c^2+d^2)(a^2+b^6+c^2+d^2)(a^2+b^2+c^6+d^2)(a^2+b^2+c^2+d^6).$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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