Question

Solution set of $x=3(mod7),p\in Z,$ is given by

• A. $\left\{3\right\}$
• B. $\left\{7p–3:p\in Z\right\}$
• C. $\left\{7p+3:p\in Z\right\}$
• D. None of these

Answer 1

The correct option is C

$\left\{7p+3:p\in Z\right\}$

Explanation for the correct answer:

The given Equation as,

$x=3(mod7),p\in Z,$

We know that

$x=a(modn)$

Then,

$x-a=p.n\left[\text{Where p}\in Z\right]$

Solving the given Equation for $x$:

$$\begin{gathered} x=3(mod7) \\ \Rightarrow x-3=0(mod7) \\ \Rightarrow x-3=7p \\ \Rightarrow x=7p+3 \end{gathered}$$

Thus, the solution set is $\left\{7p+3:p\in Z\right\}$

Therefore, the correct answer is option (C).