IMO Shortlist 1992 problem 14


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2. travnja 2012.
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For any positive integer x define g(x) as greatest odd divisor of x, and f(x) =\begin{cases}\frac{x}{2}+\frac{x}{g(x)}&\text{if\ \(x\) is even},\\ 2^{\frac{x+1}{2}}&\text{if\ \(x\) is odd}.\end{cases}
Construct the sequence x_1 = 1, x_{n + 1} = f(x_n). Show that the number 1992 appears in this sequence, determine the least n such that x_n = 1992, and determine whether n is unique.
Izvor: Međunarodna matematička olimpijada, shortlist 1992