Question: '8, EXERCISE 8.5.1: Proving divisibility results by induction. Prove each of the following statements using mathematical induction. (a) Prove that for any positive integer n,

'8, EXERCISE 8.5.1: Proving divisibility results by induction. Prove each of the following statements using mathematical induction. (a) Prove that for any positive integer n, 4 evenly divides 32n-'l. (b) Prove that for any positive integer n, 6 evenly divides 7n \"I. (c) Prove that for any positive integer n, 4 evenly divides 11\" - 7\". (d) Prove that for any positive integer n, 7 evenly divides 9\" - 2\". (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

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