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2024 AMC 10BProblem 24P21-25~5 minPrint
Modular ArithmeticNumber PropertiesApply an identity: SFFT, sum of squares, difference of cubes, VietaSplit into exhaustive cases and handle each

Let P(m)=m2+m24+m48+m88P(m)=\frac{m}{2}+\frac{m^2}{4}+\frac{m^4}{8}+\frac{m^8}{8} How many of the values P(2022)P(2022) , P(2023)P(2023) , P(2024)P(2024) , and P(2025)P(2025) are integers?

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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.