# Functional Equation!

Algebra Level 5

Let $$f$$ be a function from the non-negative integers to the positive integers with $$f(0) = f(1) = 1$$ and $\frac{f(x)f(y+1)}{f(y)} + \frac{f(x)f(x-y)}{f(x-y-1)} = f(x+1).$ Find the exponent of 3 in the prime factorization of $$f(2016)$$.

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