(1) Recall that R = ZZ is a ring for every natural number n. For example Z/2Z = {0 + 2Z, 1 + 2Z} and Z/4Z = {0 + 4Z, 1 + 4Z, 2 + 4Z, 3 + 4Z}. Show that the map Z/4Z - Z/2Z : a + 47 -> a + 2Z is a ring homomorphism. Remark: the homomorphisms Z/pntiZ -> Z/p"Z are used to define the p-adic integers as an inverse limit