Question

If $n(n^2-1)$ is divisible by $24$, then which of the following statements is true?

• A. $n$ can be any odd integral value.
• B. $n$ can be any integral value.
• C. $n$ can be any even integral value.
• D. $n$ can be any rational number.

Answer 1

The correct option is A $n$ can be any odd integral value.

$n(n^2-1)=n\ast (n-1)\ast (n+1)$
If $n$ is even, then $n-1$ and $n+1$ will be odd, therefore $n(n^2-1)$ is not divisible by 4 and therefore not divisible by 24.
Hence $n$ has to be an odd integer.