Basics of Congruence

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1) Which statement is true?

Explanation

17=7×2+3 → remainder 3.

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About This Quiz
Basics Of Congruence - Quiz

What does it mean when two numbers are “congruent” to each other? In this quiz, you’ll explore the idea of congruence, practice writing and checking statements like a ≡ b (mod n), and see how simple it is to spot when numbers share the same remainder. Take this quiz to... see moreget started with the building blocks of modular congruence. see less

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2) Which is equivalent to 25 ≡ ? (mod 6)

Explanation

25=6×4+1.

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3) If 42 ≡ r (mod 8), what is r?

Explanation

42=8×5+2.

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4) Which of the following congruences is correct?

Explanation

19=9×2+1.

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5) Which pair of numbers are congruent mod 5?

Explanation

27≡2, 32≡2 (mod 5).

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6) If x ≡ 4 (mod 6), which number could x be?

Explanation

Numbers of form 6k+46k+46k+4: 4, 10, 16, …

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7) Which congruence is true?

Explanation

50=9×5+5.

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8) Which is correct about 33 mod 11?

Explanation

33 is a multiple of 11.

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9) If a ≡ 2 (mod 7), what is a + 7?

Explanation

Adding 7 (a multiple of 7) doesn’t change the congruence class.

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10) Which of the following is equivalent to 71 mod 10?

Explanation

71=10×7+1.

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Which statement is true?
Which is equivalent to 25 ≡ ? (mod 6)
If 42 ≡ r (mod 8), what is r?
Which of the following congruences is correct?
Which pair of numbers are congruent mod 5?
If x ≡ 4 (mod 6), which number could x be?
Which congruence is true?
Which is correct about 33 mod 11?
If a ≡ 2 (mod 7), what is a + 7?
Which of the following is equivalent to 71 mod 10?
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