For n ≥ 1, use congruence theory to establish each of the following divisibility statements:
(a) 7 | 52n + 3 · 25n−2.
(b) 13 | 3n+2 + 42n + 1.
(c) 27 | 25n + 1 + 5n+2.
(d) 43 | 6n+2 + 72n + 1.
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