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
```