For n ≥ 1, use mathematical induction to establish each of the following divisibility statements:
(a) 8 | 52n + 7.
[Hint: 52(k + 1) + 7 = 52(52k + 7) + (7 − 52 · 7).]
(b) 15 | 24n − 1.
(c) 5 | 33n + 1 + 2n+l.
(d) 21 | 4n+1 +52n − 1.
(e) 24 | 2 · 7n + 3 · 5n − 5.
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