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2019 AMC 10BProblem 6P1-10~2 minPrint
Algebraic ManipulationQuadraticsApply an identity: SFFT, sum of squares, difference of cubes, VietaSet up the equation/formula and compute; no special trick needed

There is a real nn such that (n+1)!+(n+2)!=n!⋅440(n+1)! + (n+2)! = n! \cdot 440 . What is the sum of the digits of nn ?

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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.