# A functional fix

Algebra Level 5

Suppose $$f$$ is a function from the positive integers to the positive integers that satisfies

$f(n) = \begin{cases} n - 600, & \text{ for } n > 2013,\\ f( f(n + 800)), & \text{ for } n \leq 2013. \\ \end{cases}$

How many fixed points does $$f$$ have?

Details and assumptions

A fixed point of a function $$f$$ is a value $$x$$ which satisfies $$f(x) = x$$.

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