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AIME 1993 Problem 5

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Let P0(x)=x3+313x2−77x−8 P_0(x) = x^3 + 313x^2 - 77x - 8\,. For integers n≥1 n \ge 1\,, define Pn(x)=Pn−1(x−n) P_n(x) = P_{n - 1}(x - n)\,. What is the coefficient of x x\, in P20(x) P_{20}(x)\,?

Dataset text AIME 1983 to 2026. Quoted with source.

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