(12.1) Primes in the Eisenstein integers:
(a) Is 19 a prime in the Eisenstein integers? is 79? If they are, explain why,
if not, display a factorization into primes.
(b) Show that if p is a prime in the rational integers and p ≡ 2 mod 3, then
p is also a prime in the Eisenstein integers.

(PLEASE ANSWER NEATLY AND ALL PARTS OF THE QUESTION)