Bob considers a small RSA public$-$key crypto$-$system with modulus $n=91$ and the non$-$trivial

second smallest valid exponent $e.$

$($a$)$ Find Euler's totient function $(n).$

$($b$)$ Please help Bob finding the public exponent $e.$

$($c$)$ After finding $e.$ He sends the public key which is a pair $(n,e)$ to Alice. On behalf of

Alice, please encrypt the message $x=87.$ In case you cannot find $e$ in $(10$b$),$ please

assume that $(n,e)=(91,11).$

$($d$)$ Please help Bob finding the private exponent $d$ using the extended Euclid's algorithm.