I need help solving this problem.

. 1 w : Iii-IN. : _ _ - Let E 2' 1 + N3) . The ring of Eisenstein integers is Z[w] = a + Miles\" 6 3. It is a subring of C with respect to 11(1) =l1'2ls1' '5 zl'~'l , i.e., \"(a + bl\") = a: \"b + b! . Show that a prime number P $5 3 has a proper factorisation in 2M if and only if P 5 1(W3) . It may be useful to observe that there is an element in U[p) of order 3 ifand only if 12 + 1' + 1 = (1'1 ll/(l' 1) has a root in Z)! .BUT if you decide to use that observation you have to show it