Exercise 8.5.1: Proving divisibility results by induction. About Prove each of the following statements using mathematical induction. (a) Prove that for any positive integer n, 4 evenly divides 32n-1. (b) Prove that for any positive integer n, 6 evenly divides 7n - 1. (c) Prove that for any positive integer n, 4 evenly divides 11n - 7n. (d) Prove that for any positive integer n, 7 evenly divides 9n - 2n. (e) Prove that for any positive integer n, 2 evenly divides n2 - 5n 2. (f) Prove that for any positive integer n, 3 evenly divides n3 - 4n 6.