The remainder,when $7^{103}$ is divided by $17$ is $..........$.

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

The expression $2^{4n} - 15n - 1$, where $n \in N$ (the set of natural numbers), is divisible by

The numbers $a_n = 6^n - 5n$ for $n = 1, 2, 3, \ldots$ when divided by $25$ leave the remainder:

Given below are two statements:
Statement $I$: $25^{13} + 20^{13} + 8^{13} + 3^{13}$ is divisible by $7$.
Statement $II$: The integral part of $(7 + 4\sqrt{3})^{25}$ is an odd number.
In the light of the above statements, choose the correct answer from the options given below:

If $[x]$ denotes the greatest integer function of $x$,then the number of positive integral divisors of $\left[(2+\sqrt{3})^5\right]$ is