Question $5[20$ points$]$

Consider an RSA system in which $p=11$ and $q=13($n$=143).$ Answer the following questions:

$($a$)[2$ points$]$ Why can't we chose $e=35?$

$($b$)[8$ points$]$ Use Extended Euclidean algorithm and calculate $d$ when $e=13.$

$($c$)[10$ points$]$ Use repeated square method to calculate the encryption of $M=17.$