Which of these congruences is true?

45 \equiv 7 \pmod{4}

Correct answerYour answer

38 \equiv 3 \pmod{7}

Correct answerYour answer

26 \equiv 4 \pmod{6}

Correct answerYour answer

-8 \equiv 5 \pmod{6}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Check whether the modulus divides the difference.
$38 - 3 = 35 = 7 \times 5$ . The others give 38, 22 and $-13$ , which 4 and 6 do not divide.

Worth noting

$-8 \equiv 5 \pmod{6}$ fails: $-8 - 5 = -13$ .

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

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

Explanation