$1.[$COMPUTER PROBLEM$]$ Find three $$random$$ primes$-$

p$,$ q and r$-$ each of ten digits. Let m $=$ p q r$.$ You are going to

have to encrypt messages$-$ x$-$ by computing xe

mod m$,$ Find

an $$appropriate$$ random e of $20$ digits. $($Make sure this e

will work.$)$ Show how to decode messages. $($You will need to

use the computer to solve some congruences.$)$ In particular,

determine what the encoded message is if the original message is just $2.$ Show that the decryption will give the correct original message. Finally, suppose I use this method but

with three different primes and m and e$,$ which you don$$t

know, but somehow you discover that when the original message is $2$ the encrypted message is $25.$ If you then find

an encrypted message of $625,$ what was the original message?