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Found problems: 26

1969 All Soviet Union Mathematical Olympiad, 125
Given an equation $$x^3 + ?x^2 + ?x + ? = 0$$ First player substitutes an integer on the place of one of the interrogative marks, than the same do the second with one of the two remained marks, and, finally, the first puts the integer instead of the last mark. Explain how can the first provide the existence of three integer roots in the obtained equation. (The roots may coincide.)
cubic algebra