Problem $3$: Suppose that you want to encrypt a message using an affine cipher. You let $a=0,b=1,$ etc.,

but you also include $?=26$ and $27.$ Therefore you have $28$ symbols to encrypt and your affine cipher

is given by

$ax+b(mod28).$

$($a$)$ Enumerate all choices for $ain{Z}_{27}$ that allow you to decrypt.

$($b$)$ Suppose you try to use $a=14$ and $b=3.$ Find two plaintext letters that encrypt to the same ciphertext

letter.