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

MCQ

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

✓
6
B
16
C
26
D
24

✓

Answer

Correct option: A.

6

6

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

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