SOLUTION: Prove that for any integer n, {{{ n(n^2-1)(n+2) }}} is divisible by 12. Below is my attempt at trying to solve it, however I don't think example is enough to show as proof. w

Question 1070285: Prove that for any integer n, is divisible by 12.
Below is my attempt at trying to solve it, however I don't think example is enough to show as proof.
we want to prove . I written it also as
which if you plug in 2 or 3 it will give an even number in the numerator which means it can be divisible by 12.
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
.
You got this product .

The numerator is the product of 4 consecutive integers, isn't it ?

One of them is a multiple of 4. One of them is a multiple of 3.

Therefore, the numerator is a multiple of 12,

so the fraction is an integer number.

Proved.

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MOREOVER, it is a multiple of 24.

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