For all positive integers $k$,if the greatest divisor of $25^k+12k-1$ is $d$,then $4\sqrt{d}=$

The number $(101)^{100}-1$ is divisible by

If $(27)^{999}$ is divided by $7$,then the remainder is

For every natural number $n$,${3^{2n + 2}} - 8n - 9$ is divisible by

Statement $-1$: For every natural number $n$,$(n + 1)^7 - n^7 - 1$ is divisible by $7$.
Statement $-2$: For every natural number $n$,$n^7 - n$ is divisible by $7$.

If $n \in N$,then ${11^{n + 2}} + {12^{2n + 1}}$ is divisible by