Use the principle of mathematical induction to show that `a^(n) - b^n)` is divisble by `a-b` for all natural numbers n.

Explanation

To prove that \( a^n - b^n \) is divisible by \( a - b \) for all natural numbers \( n \) using the principle of mathematical induction, we will follow these steps:

### Step 1: Base Case
We first check the base case when \( n = 1 \).

\[ P(1): a^1 - b^1 = a - b \]
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