# A natural functional equation

Algebra Level 3

Find the natural number $$a$$ for which $\displaystyle \sum_{k=1}^n f(a+k)=16(2^n-1)$ where the function $$f$$ satisfies the relation $$f(x+y)=f(x)f(y)$$ for all natural numbers $$x,y$$ and furthermore $$f(1)=2.$$

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