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Question

If n is odd show that n(n21) is divisible by 24.
We have n(n21)=n(n1)(n+1).

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Solution

Since n is odd, n1 and n+1 are two consecutive even numbers; hence one of them is divisible by 2 and the other by 4.
Again n1,n,n+1 are three consecutive numbers; hence one of them is divisible by 3. Thus the given expression is divisible by the product of 2,3 and 4, that is, by 24.

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