Question

The largest number by which the expression $n^3-n$ is divisible for all possible integral values of n, is:

• A. $2$
• B. $3$
• C. $4$
• D. $5$
• E. $6$

Answer 1

The correct option is E $6$

$n^2-n=(n-1)\left(n\right)(n+1)$, for integral values of n, represents the product of three consecutive integers.

Since in a pair of consecutive integers, there is a multiple of two, and in a triplet of consecutive integers, there is a multiple of three, then $n^3-n$ is divisible by $6$.