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Modulo Arithmetic & Congruence · Question 53 of 97

Question 53

MediumOriginal question

a≡2(mod6)a \equiv 2 \pmod{6} and b≡5(mod6)b \equiv 5 \pmod{6}. What is (a−b) mod 6(a - b) \bmod 6?

Options for question 53

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. a−b≡2−5=−3(mod6)a - b \equiv 2 - 5 = -3 \pmod{6}.

  2. −3+6=3-3 + 6 = 3.

Worth noting

−3-3 must be brought into 0,…,50, \dots, 5 by adding 6.

Concept
Combining two congruences
Typical time
90 s
Your time
—
The rule this testsCongruence modulo n
Practise this chapter →

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

Practise this chapter →

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