Cool Functional Equation

Algebra Level 3

$\large{f(f(x)) = f(x) + x}$

Let $$f : \mathbb{R} \to \mathbb{R}$$ be a continuous function such that the above equation is satisfied for all $$x \in \mathbb{R}$$, and for all $$x > 0$$, we have $$f(x) > 0.$$

If $$f(1)=2014,$$ find $$f(2015).$$

This is a original problem.
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