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Modulo Arithmetic & Congruence · Question 73 of 97

Question 73

MediumOriginal question

Which of these congruences has no solution?

Options for question 73

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. ax≡b(modn)ax \equiv b \pmod{n} has a solution exactly when gcd⁡(a,n)\gcd(a, n) divides bb.

  2. gcd⁡(6,9)=3\gcd(6, 9) = 3 does not divide 4. The others: 3 divides 3; gcd⁡(2,9)=1\gcd(2, 9) = 1; gcd⁡(4,10)=2\gcd(4, 10) = 2 divides 6.

Concept
When a congruence has no solution
Typical time
90 s
Your time
—
The rule this testsSolving with congruences
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.