Use mathematical induction to prove the truth of each of the following assertions for all n ≥ 1.
(a) [BB] n3 + 2n is divisible by 3.
(b) n3 + (n + l)3 + (n + 2)3 is divisible by 9.
(c) [BB] 5n − 1 is divisible by 4.
(d) 8n − 3n is divisible by 5.
(e) 52n − 25n is divisible by 7.
(f) [BB] 10n+1 + 10n + 1 is divisible by 3.
(g) n3 + 5n is divisible by 6.
(h) 2n + 3n − 5n is divisible by 6.
(i) 16n + 10n − 1 is divisible by 25.
(j) [BB] (2n)! is divisible by 2n.
(k) an − bn is divisible by a − b for any integers a, b with a − b ≠ 0.
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