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2004 AMC 10A Problem 24

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2004 AMC 10A Problem 24AMC 10 Step by Step
Name:                             Date: September 13, 2026
Functions · difficulty 4 of 5 · about 3 min · position P21-25

Let ff be a function with the following properties:

(i) f(1)=1f(1) = 1 , and

(ii) f(2n)=n⋅f(n)f(2n) = n \cdot f(n) for any positive integer nn .

What is the value of f(2100)f(2^{100}) ?

  1. A)

    11

  2. B)

    2992^{99}

  3. C)

    21002^{100}

  4. D)

    249502^{4950}

  5. E)

    299992^{9999}

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