IMO 1978 LL FIN12

The equation x3 + ax2 + bx + c = 0 has three (not necessarily

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IMO 1978 LL FIN12

Origin: FIN

Problem

The equation x3 + ax2 + bx + c = 0 has three (not necessarily distinct) real roots t, u, v. For which a, b, c do the numbers t3, u3, v3 satisfy the equation x3 + a3x2 + b3x + c3 = 0?