In textbook RSA key generation function, assume we have chosen two primes p = 29 and q = 47.

(a) According to the key generation algorithm, can we choose integer e as e = 7? If we can choose e = 7, please explain the reason, and calculate the public key and private key of textbook RSA using extended Euclidean algorithm. If we cannot choose e = 7, please also explain the reason.