$(3k+2)^2$ leaves remainder ............ on dividing by $3$.

The $\text{g.c.d.}$ (greatest common divisor) of two numbers is $16$ and their product is $3072$. Find their $\text{l.c.m.}$ (least common multiple).

The $\text{l.c.m.}$ of two numbers is $14$ times their $\text{g.c.d.}$ and the sum of $\text{l.c.m.}$ and $\text{g.c.d.}$ is $600$. If one of the numbers is $280$,then find the other number.

Prove that the square of any odd positive integer is of the form $8m + 1$,where $m$ is a non-negative integer.

Prove that $\sqrt{p}+\sqrt{q}$ is irrational,where $p$ and $q$ are distinct prime numbers.

The last digit of $10^{n}$ for any integer $n \geq 1$ is ............