Question

For all $n\in N;n^5-n$ is divisible by

• A. $30$
• B. $240$
• C. $60$
• D. $480$

Answer 1

The correct option is A $30$

Let $P\left(n\right)=n^5-n=n(n^4-1)$
$P\left(1\right)=0=$ divisible by $30,240,60,480$
$P\left(2\right)=30=$ divisible by only $30$
Thus for $n\in N,n^2-n$ can be divisible only by $30$ in the given options.