# Function can be tricky (2)

Algebra Level 3

$\begin{cases} f(x) & = k_{1}x^{2016}+k_{2}x^{2015}+\dots+k_{2015}x^{2}+k_{2016}x+k_{2017} \\ f(2016) & = 2016 \\ f(1) & = 2016 \\ f(0) & = 2016 \end{cases}$

If $$f(x)$$ is defined that $$f(a+b)=f(ab)$$ , where $$a$$ and $$b$$ for any real numbers.

find $$(k_{1}k_{2}k_{3}\dots k_{2016}k_{2017})+(k_{1}+k_{2}+k_{3}+\dots +k_{2016}+k_{2017})$$.

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