The remainder obtained when $5^{124}$ is divided by $124$ is

For every natural number $n,$ $n(n^2 - 1)$ is divisible by

The expression $(1 + x)^n - nx - 1$ is divisible by (where $n \in N$ and $n > 1$):

If $P(n):$ " $2^{2n}-1$ is divisible by $k$ for all $n \in N$ " is true,then the value of $k$ 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 $S - k =$

$x^n + y^n$ is divisible by