# 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 \( f(x) = x \).