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Modulo Arithmetic & Congruence · Question 68 of 97

Question 68

MediumOriginal question

Which of these congruences has no solution?

Options for question 68

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

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, so 6x≡4(mod9)6x \equiv 4 \pmod{9} has none: 6x6x only leaves 0, 3 or 6.

Worth noting

4x≡6(mod10)4x \equiv 6 \pmod{10} does have solutions: x=4x = 4 gives 16≡616 \equiv 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.