If `a` and `b` are distinct integers, prove that `a - b` is a factor of `a^n-b^n`, whenever n is a positive integer.

Explanation

To prove that \( a - b \) is a factor of \( a^n - b^n \) for distinct integers \( a \) and \( b \) when \( n \) is a positive integer, we can use the Binomial Theorem. Here’s a step-by-step solution:

### Step 1: Start with the expression \( a^n - b^n \)
We want to show that \( a - b \) divides \( a^n - b^n \).

### Step 2: Rewrite \( a^n - b^n \)
Using the identity for the difference of powers, we can express \( a^n - b^n \) as:
\[
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