linear congruential pseudorandom number generator question

From: Korejwa (korejwa_at_tiac.net)
Date: 04/30/05 

Date: Sat, 30 Apr 2005 05:49:15 GMT

If I have a sequence of numbers that I know were generated by a linear
congruential pseudorandom number generator, how can I calculate the
internal state of the generator?

The pseudorandom number generator performs this function:

X = (A * X + C) MOD N
return a value which reduces X to the range of a specified Min-Max value.

A, C, and N are known constants. X is modified each time the function is
called.

Using algebra, I can calculate a range of possible values that X could be
for any given output. Each consecutive output reduces the set of possible
X values exponentially, until only one possibility remains. But how do
you calculate the reduced set of possible X values for each known
consecutive output?

I hope my poor description of this problem is clear enough. I'm sure it
has a solution and many people have examined it before.