# A problem from RMO 2006

Algebra Level 3

Let $$X$$ denote the set of all natural numbers greater than or equal to 8. Let $$f :X\rightarrow X$$ be a function that satisfies $$f(x+y)=f(xy)$$ for all positive integers $$x$$ and $$y$$ greater than or equal to 4. If $$f(8)=9$$, then find the value of $$f(9)$$.

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