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For any integer n ≥ 1, let be the statement that is divisible by 9.
Base case. The statement says that is divisible by 9, which is true.
Inductive Step. Fix k ≥ 1, and suppose that holds, that is, is divisible by 9,
It remains to show that holds, that is, is divisible by 9,
Thus, by the principle of mathematical induction, for all n ≥ 1, holds.
Therefore is divisible by 9 for all positive integers n.
Therefore is divisible by 3 for all positive integers n.