João's functional equation

Algebra Level 2

Let \( f \) be a function from the positive integers to the positive integers that satisfies the property \[ f (x + y) = f (x) f (y) \]

for all pairs of positive integers \((x,y) \). If we are given that \( f(2) = 9 \), what is the value of \( f(5) \)?

This problem is posed by João B.

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