You are trying to encrypt using the affine function $13$x $+22$ mod $26.$

$($a$)$ Encrypt HATE and LOVE. Why is decryption impossible?

$($b$)$ Find two different three$-$letter words that encrypt to WWW$.$

$($c$)$ Challenge: Find a word $($that is legal in various word games$)$ that encrypts to JJJ$.$

$($There are four such words.$)$