For every natural number $n,$ $n(n^2 - 1)$ is divisible by

The remainder obtained when $5^{99}$ is divided by $13$ is

The remainder on dividing $1+3+3^{2}+3^{3}+\ldots+3^{2021}$ by $50$ is

Let $a, b, c, d$ be positive integers. Consider the following statements:
$I$. If $9$ divides $a^3+b^3+c^3$,then $3$ divides $abc$.
$II$. If $9$ divides $a^3+b^3+c^3+d^3$,then $3$ divides $abcd$.

The remainder on dividing $5^{99}$ by $11$ is

The remainder left when $8^{2n} - 62^{2n+1}$ is divided by $9$ is: