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2019 AMC 10A Problem 25

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2019 AMC 10A Problem 25AMC 10 Step by Step
Name:                             Date: September 13, 2026
Divisibility & Factors · difficulty 5 of 5 · about 10 min · position P21-25

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 .)

  1. A)

    3131

  2. B)

    3232

  3. C)

    3333

  4. D)

    3434

  5. E)

    3535

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