Consider the statement: For any positive integer nn, n3+2nn3+2n is a multiple of 33. Set up the framework for a proof by mathematical induction by doing the following steps: State the base case, and prove that the base case is true. Clearly state the inductive hypothesis. Clearly state the inductive step (that is, clearly state what needs to be proven following the inductive hypothesis). Give at least one suggestion for how a full proof of the inductive step might go, that is reasonable and likely to be useful.

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