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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