$($a$)$ Show that $937$ is the inverse of $13$ modulo $2436.$

$\%$

$($b$)$ Using the fast modular exponentiation algorithm, show that $(1947{)}^{937}$

mod$(2537)$ is $1121$mod$(2537).$

$\%$

$(2$ marks$)$

$($c$)$ We received the encrypted message $1947.$ Show that the decrypted mes$-$

sage is $LV,$ if it was encrypted using the RSA cipher with key $(2537,13)?$