Quote:
Originally Posted by robert44444uk
Anyway, I would proposed based on extremely limited observations that such integers exist and further, there are infinite integers that are never mod values.

There is no such thing as an "infinite" integer. Perhaps you mean "infinitely
many"???
The question you ask (rephrased) is whether the range of F_n mod F_m is Z.
This is a somewhat interesting question. I will look into it if I can find
the time.
A secondary question would be to ask for the DENSITY (in Z) of the set F_n mod F_m if it is not all of Z.