IMO 1992 LL IRE33

Let a, b, c be positive real numbers and p, q, r complex numbers.

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IMO 1992 LL IRE33

Origin: IRE

Problem

Let a, b, c be positive real numbers and p, q, r complex numbers. Let S be the set of all solutions (x, y, z) in C of the system of simultaneous equations ax + by + cz = p, ax2 + by2 + cz2 = q, ax3 + bx3 + cx3 = r. Prove that S has at most six elements.