Basics of Modular Arithmetic

If $k+9\equiv 4(\mathrm{mod} 5)$, then $k$ can be _____.

Set of residue classes modulo $5$ is

Set of residue classes modulo $4$ is

If $k+9\equiv 3(\mathrm{mod} 6)$, then $k$ can be _____.

If $k+9\equiv 4(\mathrm{mod} 5)$, then $k$ can be _____.

If $k+7\equiv 2(\mathrm{mod} 4)$, then $k$ can be _____.

If $k+9\equiv 2(\mathrm{mod} 7)$, then $k$ can be _____.

What is $9\mathrm{mod}3?$

Which of the following is a common solution of $3\mathrm{x}\equiv 2\left(\mathrm{mod} 5\right)$ and $4\mathrm{x}\equiv 0\left(\mathrm{mod} 6\right)$?

If ${\mathrm{x}}^3\equiv \mathrm{x}(\mathrm{mod} 3)$, then $x$ can be _____.

Find the least positive value of $x$ if $\mathrm{x}+15\equiv 4(\mathrm{mod} 8)$.

Find the least positive value of $x$ if $\mathrm{x}+13\equiv 2(\mathrm{mod} 8)$.

Find the remainder when ${11}^2$ is divided by $7$.

Find the remainder when $8^{15}$ is divided by $5$.

Find the remainder when $3^{21}$ is divided by $5$.

Find the least positive value of $x$ if $\mathrm{x}+12\equiv 1(\mathrm{mod} 8)$.

Find the least positive value of $x$ if $\mathrm{x}+10\equiv 1(\mathrm{mod} 8)$.

If $8-8-2009$ is a Saturday, then $15-8-2010$ falls on _____.

Find the remainder when $9^{11}-9$ is divided by $11$.

Find the remainder when $5^{11}-5$ is divided by $11$.