Recall that a way of simulating a sequence x$1,$ x$2,...$ pseudorandom numbers

is via a linear congruential generator $($LCG$),$

xj$+1=$ axj $+$ b mod m$.(1)$

$($a$)(6$ marks$)$ Write a function with inputs n$,$ a$,$ b$,$ m$,$ s to produce a sequence of n $($i$.$e$.$ list$/$array of length n$)$ pseudorandom numbers according

to $(1)$ with seed s $($i$.$e$.$ x$0=$ s$).$

$($b$)(2$ marks$)$ Demonstrate your function works by creating a list of $20$

pseudorandom numbers with a $=51$ and b $=13,$ m $=2^8+1,$ s $=7.$

$($c$)(2$ marks$)$ Why would the choice of parameters a $=2,$ b $=4,$ m $=8$ be

a bad choice for creating pseudorandom numbers?