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2025 AMC 10BProblem 10P1-10~4 minPrint
PolynomialsDivisibility & FactorsApply an identity: SFFT, sum of squares, difference of cubes, VietaSet up the equation/formula and compute; no special trick needed

Let f(n)=n3−5n2+2n+8f(n)=n^3-5n^2+2n+8 and g(n)=n3−6n2+5n+12.g(n)=n^3-6n^2+5n+12. What is the sum of all integers nn such that f(n)g(n)\tfrac{f(n)}{g(n)} is an integer?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.