# 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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