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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