COMC 2023 C Problem 1

Let F be a function which maps integers to integers by the following rules:

F(n)=n-3 if n \geq 1000;

F(n)=F(F(n+5)) if n<1000.

(a) Find F(999).

(b) Show that F(984)=F(F(F(1004))).

(c) Find F(84).