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Determine all quadruples (a, b, c, d) of real numbers

Source: Austrian Mathematical Olympiad 1997, Part 2, D2, P1

July 4, 2011
inequalitiesinequalities proposed

Problem Statement

Determine all quadruples (a,b,c,d)(a, b, c, d) of real numbers satisfying the equation 256a3b3c3d3=(a6+b2+c2+d2)(a2+b6+c2+d2)(a2+b2+c6+d2)(a2+b2+c2+d6).256a^3b^3c^3d^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).
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