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For every natural number n, the expression 41ⁿ − 14ⁿ is divisible by which of the following?

1. 26
2. 27
3. 25
4. None of these

Correct answer: 27

Solution

For any natural n, a^n - b^n is divisible by a - b. Here 41 - 14 = 27, so 41^n - 14^n is always divisible by 27.

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