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

If $n \in N$,then ${x^{2n - 1}} + {y^{2n - 1}}$ is divisible by

The sum of the squares of three consecutive odd numbers increased by $1$ is divisible by-

If the greatest divisor of $30 \cdot 5^{2n} + 4 \cdot 2^{3n}$ is $p, \forall n \in N$ and that of $2^{2n+1} - 6n - 2$ is $q, \forall n \in N$, then $p+q=$

$7^{2n} + 16n - 1$ $(n \in N)$ is divisible by

If $n > 1$ is an integer and $x \neq 0$, then $(1+x)^{n}-nx-1$ is divisible by