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Modulo Arithmetic & Congruence · Question 62 of 97

Question 62

EasyOriginal question

A number multiplied by 4 leaves remainder 1 on division by 7. What is the least positive such number?

Options for question 62

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. We need 4x≡1(mod7)4x \equiv 1 \pmod{7}.

  2. 4×2=8=7+14 \times 2 = 8 = 7 + 1, so x=2x = 2.

Worth noting

1 gives 4×1=44 \times 1 = 4, which leaves 4, not 1.

Concept
A linear congruence
Typical time
60 s
Your time
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The rule this testsSolving with congruences
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Ten questions from Modulo Arithmetic & Congruence, at your own pace.

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