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2018 AMC 10AProblem 7P1-10~3 minPrint
Exponents, Logarithms & RadicalsDivisibility & FactorsSplit into exhaustive cases and handle eachSet up the equation/formula and compute; no special trick needed

For how many (not necessarily positive) integer values of nn is the value of 4000⋅(25)n4000\cdot \left(\tfrac{2}{5}\right)^n 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.