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For each natural number n, the expression n(n² - 1) is always divisible by which of the following?

1. 4
2. 6
3. 10
4. None of these

Correct answer: 6

Solution

The expression n(n² - 1) can be factored as n(n - 1)(n + 1), which represents the product of three consecutive integers. Since among any three consecutive integers, at least one is divisible by 2 and at least one is divisible by 3, the entire product is always divisible by 6.

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