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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