4. For n > 1, use mathematical induction to establish each of the following divisibility statements: (a) 8|52n + 7. [Hint: 52(k+1) + 7 = 5?(5k + 7) + (7 – 52 . 7).] (b) 15|24" – 1. (c) 5|33n+1 + 2"+1....

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Extracted text: 4. For n > 1, use mathematical induction to establish each of the following divisibility statements: (a) 8|52n + 7. [Hint: 52(k+1) + 7 = 5?(5k + 7) + (7 – 52 . 7).] (b) 15|24" – 1. (c) 5|33n+1 + 2"+1. (d) 21 |4"+1 + 52n-1. (e) 24 |2.7" + 3.5" – 5.