Problem $1.(100$ points$)$

In a public$-$key system using RSA, perform encryption and decryption for the following $p,q,e,$ and $M$ : $p=5$;$q=11,e=3$;$M=9$

$(1)$ Show encryption process. $(25$ points$)$

$(2)$ Calculate private key $d$ using three different methods learnt from class to be used for decryption. $(45$ points$)$

$(2\mathrm{.}1)$ First Method. $(15$ points$)$

$2$