# Congruential Generators.

#### Cynderella

##### New Member
Find all of the cycles of the following congruential generators. For each
cycle identify which seeds $$X_0$$ lead to that cycle.
$$(a). X_{n+1} = 9X_n + 3\mod 11$$
$$(b). X_{n+1} = 8X_n + 3\mod 11$$
$$(c). X_{n+1} = 8X_n + 2\mod 12$$

How can i choose the seed,$$X_0$$, at random ?

###When will i stop to generate numbers ?

I supposed to draw $$X_0$$ at random from $$0$$ to $$10$$ [since $$m=11$$]and wrote R codes :

Code:
      X<- 0
X[1]<-8 # seed ,Xo

for(i in 2:11){
X[i]<-(9*X[i-1]+3)%%11
cat("",9*X[i-1]+3,"",X[i],"\n")
}

X
How can i solve the problem ?