Let R=Z[\sqrt{-5}]

a) Show that:
i) \langle 2 \rangle = \langle 2, 1 + \sqrt{-5} \rangle^2
ii) \langle 3 \rangle = \langle 3, 1 + \sqrt{-5} \rangle \langle 3, 1 - \sqrt{-5} \rangle

b) Prove that all ideals that appear on the right in equations of part a) are prime using that R/\langle 2 \rangle have four elements.