Problem:
Define a function on the positive integers recursively by , if is even, and if is odd and greater than 1 . What is
Answer Choices:
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Solution:
It is clear after listing the first few values, , , and so on, that for all positive integers . Indeed, the function is uniquely determined by the recursive description, and the function defined by fits the description. Therefore .
The problems on this page are the property of the MAA's American Mathematics Competitions