Read the two statements and choose the correct option. I. a ≡ b (mod n) exactly when a and b leave the same remainder on division by n. II. If a ≡ b (mod n), then a ≡ b (mod 2n).

Modulo Arithmetic & Congruence · Question 52 of 97

Question 52

MediumOriginal question

Read the two statements and choose the correct option.
I. $a \equiv b \pmod{n}$ exactly when $a$ and $b$ leave the same remainder on division by $n$ .
II. If $a \equiv b \pmod{n}$ , then $a \equiv b \pmod{2n}$ .

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

I: if $a = nq_1 + r$ and $b = nq_2 + r$ , then $a - b = n(q_1 - q_2)$ , and the reverse also holds. True.
II: $1 \equiv 4 \pmod{3}$ , but $4 - 1 = 3$ is not a multiple of 6. False.

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

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