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For each positive integer n, the number 7ⁿ − 3ⁿ is divisible by which of the following?

1. 7
2. 3
3. 4
4. 5

Correct answer: 4

Solution

The expression 7ⁿ − 3ⁿ can be factored and analyzed for divisibility. For any positive integer n, both 7ⁿ and 3ⁿ are odd, making their difference even, and specifically, it can be shown that it is divisible by 4.

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