4

Part of 1997 Federal Competition For Advanced Students, P2

Problems(1)

quadruples (maybe posted before)

Source: Austria 1997

Determine all quadruples

(a,b,c,d)

of real numbers satisfying the equation: 256a^3 b^3 c^3 d^3\equal{}(a^6\plus{}b^2\plus{}c^2\plus{}d^2)(a^2\plus{}b^6\plus{}c^2\plus{}d^2)(a^2\plus{}b^2\plus{}c^6\plus{}d^2)(a^2\plus{}b^2\plus{}c^2\plus{}d^6).

algebra unsolvedalgebra