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2020 AMC 10AProblem 17P16-20~6 minPrint
Absolute Value & InequalitiesNumber PropertiesPolynomialsUse an invariant, parity, or coloring argumentCompute small cases, spot the pattern, generalize

Define P(x)=(x−12)(x−22)⋯(x−1002).P(x) =(x-1^2)(x-2^2)\cdots(x-100^2). How many integers nn are there such that P(n)≤0P(n)\leq 0 ?

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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.