Question

The solution of: $8\mathrm{mod}x\equiv 6\mathrm{mod}14$ is,

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

Answer 1

The correct option is C $6,13$

Solution:-

$8x\equiv 6\left(mod14\right)$

$\because gcd(8,14)=2\text{divides}6$

To find solutions, we first solve

$8x-14y=6$

By trial and error method, we find a solution

$(x,y)=(6,3)$

This means that $x\equiv 6\left(mod14\right)$ is a solution

To the congruence $8x\equiv 6\left(mod14\right)$

$\therefore$ Incongruent solutions are,

$x=6+(k\times \frac{14}{2});k=0,1$

$\therefore x=6,13$

Hence option $C$ is the answer.