On a practice exam for a course on stochastic simulations I encountered the following question:
Show that the least significant $n$ bits must repeat with a period $2^n$ for a congruential random generator with a period $2^m$ where $m > n$.
I couldn't find an answer on how to do this anywhere. How can I shows this? Is it just that the $n$ bits can only generate $2^n$ numbers?