Please use the formula $y=(x+12)mod26$ to encrypt or decrypt the following plaintext and ciphertext. $($a$)$ Plaintext "discrete" to ciphertext, $($b$)$ Plaintext "mathematics" to ciphertext, $($c$)$ Ciphertext "otgzs teuzs" to plaintext. $(6$ points, $2$ points for each question, one word wrong and all wrong$)$

For any $n$ belongs to positive integer, prove that the integer $8n+3$ and $5n+2$ are relatively prime. $(6$