Question

The solution of $8x\equiv 6\left(mod14\right)$ is

• A. $\{8,6\}$
• B. $\{6,14\}$
• C. $\{6,13\}$
• D. $\{8,14,6\}$

Answer 1

The correct option is C $\{6,13\}$

Since,$8x\equiv 6\left(mod14\right)$
i.e., $8x-6=14k$ for $k\in I$.
$\Rightarrow 8x=14k+6$
$\Rightarrow 4x=7k+3$
The values $6$ and $13$ satisfy this equation (when $k=3$ and $k=7$),

while $8,14$ and $16$ do not.