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2004 AMC 10AProblem 24P21-25~3 minPrint
FunctionsSequences & SeriesCompute small cases, spot the pattern, generalizeCollapse a sum or product by cancellation

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}) ?

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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. Also appeared as 2004 12A #17.