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

If $a, b$ and $n$ are natural numbers, then $a^{2n-1} + b^{2n-1}$ is always divisible by:

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

For $n \in N$,the largest positive integer that divides $81^n + 20n - 1$ is $k$. If $S$ is the sum of all positive divisors of $k$,then $S - k =$

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

Let $n \in \mathbb{N}$. Which one of the following is true?