Question

Find the number of integer solutions of $9x$ $\equiv$ $2\left(\text{mod}63\right)$.

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

The correct option is D $0$

$9x$ $\equiv$ $2\left(\text{mod}63\right)$
$9x-2=63n$, for some integer $n$
$9x=63n+2$
$x=\frac{63n+2}{9}=7n+\frac{2}{9}$
Since $7n$ is an integer, $(7n+\frac{2}{9})$ cannot be an integer.
$\therefore$ It has no integer solution.