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AIME 2020a Problem 11

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For integers a,b,ca,b,c and d,d, let f(x)=x2+ax+bf(x)=x^2+ax+b and g(x)=x2+cx+d.g(x)=x^2+cx+d. Find the number of ordered triples (a,b,c)(a,b,c) of integers with absolute values not exceeding 1010 for which there is an integer dd such that g(f(2))=g(f(4))=0.g(f(2))=g(f(4))=0.

Dataset text AIME 1983 to 2026. Quoted with source.

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