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2019 AMC 10AProblem 25P21-25~10 minPrint
Divisibility & FactorsBasic CountingPrimesBound the quantity above/below or estimate to pin it downCount the complement and subtract from the totalCompute small cases, spot the pattern, generalize

For how many integers nn between 11 and 5050 , inclusive, is (n2−1)!(n!)n\frac{(n^2-1)!}{(n!)^{n}} an integer? (Recall that 0!=10!=1 .)

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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.