A function F is such that this relationship holds for all real x.

F(x) = F(398-x) = F(2158-x) = F(3214-x)

What is the maximum number of distinct values that can appear in the list F(0), F(1), F(2), ..., F(999).

(In reply to

Do I miss something? by Ady TZIDON)

While I haven't worked this out, I think that there is more to it than this.

If it said F(x) = F(398-x) = F(1399-x), for instance, I think that there might only be one distinct value possible for any integer x. The Greatest Common Divisor is going to come into play here.