João's functional equation

Algebra Level 2

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

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

This problem is posed by João B.

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