$[$COMPUTER PROBLEM$]$ Find three "random" primes$-p,q$ and $r-$ each of ten digits. Let $m=pqr.$

You are going to have to encrypt messages$-x-$ by computing $x^e$ 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?