The solution set of the congruence x equiv 3 | vedclass

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Question

(C) The given congruence relation is $x \equiv 3 \pmod{7}$.By the definition of modular arithmetic, $x \equiv a \pmod{n}$ implies that $x - a$ is a mu

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

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(C) The given congruence relation is $x \equiv 3 \pmod{7}$.By the definition of modular arithmetic, $x \equiv a \pmod{n}$ implies that $x - a$ is a multiple of $n$, such that $x - a = np$ for some integer $p \in Z$.Therefore, $x - 3 = 7p$ for some integer $p \in Z$.Rearranging the equation to solve for $x$, we get $x = 7p + 3$.Thus, the solution set is $\{7p + 3 : p \in Z\}$.

The solution set of the congruence $x \equiv 3 \pmod{7}$ is given by:

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