To become familiar with the RSA system, take the $($unrealistically small$)$ primes $p_1=7$ and $p_2=11.$

$4\mathrm{.}2\mathrm{.}1$ Explain why $e=5$ is not a valid encryption exponent.

$4\mathrm{.}2\mathrm{.}2$ Show that $e=13$ is a valid encryption exponent and compute the corresponding decryption exponent $d$ using the Euclidean algorithm.

$4\mathrm{.}2\mathrm{.}3$ Show that $e=61$ is also a valid encryption exponent, but unsatisfactory because $m^{61}-=m(mod77)$ for all $m0(mod77).$