If a, b E Z* and god(a, b) = 1, find the following: (a) god(a, a + 1) (b) god(a, a + 2) (c) god(a + b, a - b) (d) god(3a + 2, 5a + 3) (e) god(a + 2b, 2a + b) Give a complete proof to each problem. (a) Let a be an integer. Show that if 2| a and 3|a, then 6|a. (b) Suppose that a, b E Z, god(a, b) = 1, and clab. Prove that there are integers d and e such that c = de, dla, and 6|a