Given below are two statements:

Statement I: $5$ divides $n^5-n$ whenever $n$ is a nonnegative integer.

Statement II: $6$ divides $n^3-n$ whenever $n$ is a nonnegative integer.

In the light of the above statements, choose the correct answer from the options given below:

Statement I:

We need to check whether $5$ divides $n^5-n$.

By Fermat's theorem,

$n^5\equiv n\pmod 5$

So,

$n^5-n\equiv 0\pmod 5$

Therefore, $5$ divides $n^5-n$.

So, Statement I is correct.

Statement II:

$n^3-n=n(n-1)(n+1)$

This is the product of three consecutive integers.

In any three consecutive integers, one number is divisible by $3$ and at least one number is divisible by $2$.

So, the product is divisible by $6$.

Therefore, $6$ divides $n^3-n$.

So, Statement II is also correct.