The remainder when $3^{2022}$ is divided by $5$ is

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

If the expression $5^{2n} - 48n + k$ is divisible by $24$ for all $n \in N$,then the least positive integral value of $k$ is

The value of the greatest positive integer $k$,such that $49^k + 1$ is a factor of $48(49^{125} + 49^{124} + \ldots + 49^2 + 49 + 1)$ is

The expression $x(x^{n-1} - na^{n-1}) + a^n(n-1)$ is divisible by $(x-a)^2$ for:

If $2^{4n+3} + 3^{3n+1}$ is divisible by $P$ for all natural numbers $n$,then $P$ is