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Prove the following by the principle of mathematical induction: `n^3-7n+3` is divisible 3 for all `n in N`.

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To prove that \( n^3 - 7n + 3 \) is divisible by 3 for all \( n \in \mathbb{N} \) using the principle of mathematical induction, we will follow these steps: ### Step 1: Base Case We first check the base case when \( n = 1 \). \[ P(1) = 1^3 - 7 \cdot 1 + 3 = 1 - 7 + 3 = -3 \] ...
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