If $f$ is a strictly increasing function from the naturals to the naturals, and $f(f(x))=3x$, what are all values of $f(2012)$? I have only proven that $f(3x)=3f(x)$ but that get's nowhere :(
Functional Equation with Value
5
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functional-equations
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0What if you wait for one more year? Can you use your partial result then...btw: Can you show us how you have proven it? – 2012-07-23
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2I suggest that you start by looking at $f(x)$ for small values of $x$; look for a pattern when $x$ is written in base 3. – 2012-07-23