# Function in Bulk

Algebra Level 4

Let $$f(x)=ax+b$$, where $$a$$ and $$b$$ are integers, $$f^2 (0) =f(f(0))=0$$ and $$f^3 (2) = f(f(f(2)))=9$$.

Find $f^4(1)+ f^4(2)+ f^4(3)+\cdots+ f^4(2016)$

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