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The difference between an integer and its cube is divisible by
Option: 1
4

Option: 2
6

Option: 3
9

Option: 4
None of these

Answers (1)

best_answer

Let the number is x.

Then $x-x^3=x\left(1-x^2\right)=(1-x)(x)(1+x)$

According to Langrange's theorem it is divisible by 3! i.e., 6.

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