If $11^{12}-11^2=k(5 \times 10^9+6 \times 10^9+33 \times 10^8+110 \times 10^7+\ldots+33)$,then $k=$

The remainder,when $3^{2003}$ is divided by $28$,is

If $n \in N$,then ${7^{2n}} + {2^{3n - 3}} \cdot {3^{n - 1}}$ is always divisible by

The remainder when $(11)^{1011} + (1011)^{11}$ is divided by $9$ 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 $abcd$.

If $3^{2n+2}-8n-9$ is divisible by $2^p$ for all $n \in N$,then the maximum value of $p$ is