Question $1$ Show that if $n$ is pseudo$-$prime to $2in{Z}_n^{**},$ then $N=2^n-1$ is a

pseudo$-$prime to $2in{Z}_N^{**}$ as well.

Question $2$ More generally, show that if $n$ is a pseudo$-$prime to $bin{Z}_n^{**},$ and if

$gcd(b-1,n)=1,$ then the integer $N=\frac{b^n-1}{b-1}$ is pseudo$-$prime to $bin{Z}_N^{**}$ as well.

Question $3$ Based on the previous sub$-$questions, construct EXPLICITLY a sequence

$a_n$ satisfying that AAninN,$a_n$ is a pseudo$-$prime with respect to $5($i$.$e$.,5^{a_n-1}-=1mod{a}_n).$