A function F is such that this relationship holds for all real x.
F(x) = F(398x) = F(2158x) = F(3214x)
What is the maximum number of distinct values that can appear in the list F(0), F(1), F(2), ..., F(999).
Using the first equality only f(0) = f(398), f(1) = f(397), . . . f(198) = f(200), f(199) = f(199) then the sequence repeats in reverse order. That's 200 values.
From the last equality f(57) = f(999), f(58) = f(998), . . . f(398) = f(658). But using the first equality, f(57) = f(341), f(58) = f(340), . . ., down to f(398) = f(0) and we've counted those already.
Offhand I don't see how to reduce the range 399<=x<=657. That's 259 more values for a total of 459 possible distinct values assuming I haven't miscounted.

Posted by xdog
on 20140915 13:04:35 