Question $4$: $(25$ pts$)$ We want to design a mixed congruential random number generator for a microcomputer with a $16-$bit word. What would you choose as modulus $m?$ Explain the reason for your selection.

Using $a=25,c=14,$ and the initial seed of $999,$ generate three random numbers. Can you determine how many random numbers will be generated before they start repeating?