Which set is the residue class $[3]$ modulo 7?

\{3, 10, 17, 24, \dots\}

Correct answerYour answer

\{\dots, -11, -4, 3, 10, 17, \dots\}

Correct answerYour answer

\{0, 3, 6, 9, \dots\}

Correct answerYour answer

\{\dots, -10, -3, 4, 11, \dots\}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$[3]$ is every integer that leaves 3 on division by 7: $7k + 3$ for every integer $k$ , negative ones included.
$k = -2, -1, 0, 1, 2$ give $-11, -4, 3, 10, 17$ .

Worth noting

$\{3, 10, 17, 24, \dots\}$ stops at 3 and leaves out $-4$ and $-11$ .

Ten questions from Modulo Arithmetic & Congruence, at your own pace.

Ten questions from Modulo Arithmetic & Congruence, at your own pace.

Which set is the residue class [3][3][3] modulo 7?