If n N, then n(n^2− 1) is divisible by: - Vidyadip

MCQ

If $n \in N,$ then $n(n^2− 1)$ is divisible by:

✓
$6$
B
$16$
C
$26$
D
$24$

✓

Answer

Correct option: A.

$6$

$\ce{n(n^2 − 1)= n(n − 1)(n + 1)}$
One of the $\ce{n, n + 1}$ and $n − 1$ will be a multiple of $3.$
Since $\ce{n − 1, n}$ and $n + 1$ are three consecutive integers,
therefore at least one of them will be divisible by $2.$
Therefore $\ce{n(n^2 − 1)}$ is divisible by $6.$

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