# Reverse Engineer Something

Algebra Level 3

If the function $$f$$ satisfies the relation $$f\left( x+y \right) = f\left( x \right) f\left( y \right)$$ for all natural numbers $$x,y$$

And if $$f\left( 1 \right) =2$$, and for a natural number $$a$$, the summation below is satisfied.

$$\large \displaystyle \sum _{ r=1 }^{ n }{ f\left( a+r \right) } =16\left( { 2 }^{ n }-1 \right)$$

What is the value of $$a$$?

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