Souleekeen's Problem

Algebra Level 4

Consider a function \( f\colon \mathbb N \rightarrow \mathbb N \) satisfying \(f^3(x) + f^2(x) + f(x) = 3x + a \) and \(f^{2016}(2016) = 18144 \) for some constant \(a\). Find the value of \(f^{2015}(2015) - a \).

Clarification: \(f^n (x)\) denotes the function composition, \( f^n(x) = \underbrace{ f\circ f\circ f \circ \cdots \circ f}_{n \text{ number of } f\text{'s}} (x) \).

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