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Using the principle of mathematical induction to show that `41^n-14^n` is divisible by 27

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To prove that \( 41^n - 14^n \) is divisible by 27 for all natural numbers \( n \) using the principle of mathematical induction, we will follow these steps: ### Step 1: Base Case We start by checking the base case for \( n = 1 \). \[ P(1) = 41^1 - 14^1 = 41 - 14 = 27 \] ...
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