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AIME 2023a Problem 9

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Find the number of cubic polynomials p(x)=x3+ax2+bx+c,p(x) = x^3 + ax^2 + bx + c, where a,b,a, b, and cc are integers in {−20,−19,−18,…,18,19,20},\{-20,-19,-18,\ldots,18,19,20\}, such that there is a unique integer m≠2m \not= 2 with p(m)=p(2).p(m) = p(2).

Dataset text AIME 1983 to 2026. Quoted with source.

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