For ZI√51 a) determine two different (be sure to justify why they're different) factorizations of 4 into irreducibles in ZI√51 b) establish that 3 + 2√5 and −56 +25√5 are associates in ZI√51 c) Suppose P is a prime in Z, and p=N(y), some a € Z|√5| (so if y = a +b√5,N(y) = (a+b√5)(a − b√5) = a² - 5b² prove that p=I 1 mod10 d) determine a particular p++/- 1 mod 10 and a BEZ[√5] with N(B)=+/-p² then use it to deduce that Z[√5] is not a UFD (unique factorization domain) e)factorize both 11 and 19 into irreducibles in Z[√5]