Consider linear, congruential random number generators.
If **c=0**, it is obvious
that is not a good candidate integer for the initial seed because it
maps to itself. In fact, if **m = p**, a prime, then there is always a number
which maps to itself (a constant sequence), even if . Prove this by
finding the integer which maps to itself, and which does not appear in the full
period sequence of length **m-1** for the following linear, congruential
generators:

(a)(b)

(c)