A functional fix

Algebra Level 5

Suppose ff is a function from the positive integers to the positive integers that satisfies

f(n)={n600, for n>2013,f(f(n+800)), for n2013. 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 ff have?

Details and assumptions

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

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