Modular Arithmetic Quiz: Explore Congruence Concepts

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Quizzes Created: 7682 | Total Attempts: 9,547,133
| Questions: 20 | Updated: Dec 16, 2025
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1) When 25 is divided by 6, what is the remainder?

Explanation

6 × 4 = 24 → 25 − 24 = 1 → remainder = 1.

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About This Quiz
Modular Arithmetic Quiz: Explore Congruence Concepts - Quiz

Ever notice how numbers seem to loop back on themselves? This quiz takes you into modular arithmetic, where remainders create patterns that repeat in surprising ways. You’ll compare values, spot cycles, and see how congruence makes tricky ideas feel simple. Dive in and explore how numbers behave when everything works... see morein a loop.
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2) 17 is congruent to 3 modulo 7.

Explanation

17 − 14 = 3 → 17 mod 7 = 3 → congruent.

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3) If 42 mod 8 = r, then r = __

Explanation

8 × 5 = 40 → 42 − 40 = 2 → remainder 2.

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4) Which statement is correct for 19 modulo 9?

Explanation

9 × 2 = 18 → 19 − 18 = 1 → remainder 1.

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5) Which pairs of numbers are congruent modulo 5?

Explanation

Difference multiple of 5 → true for (17,22), (30,35), (40,45).

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6) If x mod 6 = 4, what is (3x) mod 6?

Explanation

x=6k+4 → 3x=18k+12=6(3k+2) → remainder 0.

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7) If a is congruent to b modulo n, then a minus b is divisible by n.

Explanation

a−b=n×t → divisible by n.

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8) Given 100 mod 12 = 4, compute (2 × 100) mod 12 = __

Explanation

2×100 mod 12 = 2×4 mod 12 = 8.

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9) Which property holds for all integers a, b, and positive integer n?

Explanation

Addition and multiplication work under modular arithmetic.

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10) Select all valid congruence statements.

Explanation

Check by division → true for a,b,d.

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11) If 8 mod 3 = 2, compute (4 × 8) mod 3.

Explanation

8 mod 3 = 2 → 4×2=8 → 8 mod 3 = 2.

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12) If A is congruent to B modulo n, then kA is congruent to kB modulo n for any integer k.

Explanation

Multiply both sides by k → congruence holds.

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13) Find the multiplicative inverse of 3 modulo 7.

Explanation

3×5=15→15 mod 7=1→inverse=5.

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14) Solve 7x congruent to 3 modulo 5. What is x modulo 5?

Explanation

7≡2(mod5)→2x≡3→inverse(2)=3→x≡9≡4.

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15) Which linear congruences have exactly one solution modulo m?

Explanation

Unique solution iff gcd(a,m)=1 → true for (a,b).

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16) Solve 5x ≡ 10 (mod 15). List least residues.

Explanation

Divide by 5→x≡2(mod3)→x=3t+2→2,5,8.

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17) A clock shows 7:00. What time will it show 137 hours later?

Explanation

137 mod 12=5→7+5=12→1:00.

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18) Every linear congruence ax ≡ b (mod m) has a solution if gcd(a,m)=1.

Explanation

Inverse exists when gcd(a,m)=1.

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19) Select all true statements about exponent patterns and last digits.

Explanation

Patterns verified by modular repetition.

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20) Find the last digit of 13^45.

Explanation

Last digit cycle for 3: 3,9,7,1 (length 4). 45 mod4=1→digit=3.

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When 25 is divided by 6, what is the remainder?
17 is congruent to 3 modulo 7.
If 42 mod 8 = r, then r = __
Which statement is correct for 19 modulo 9?
Which pairs of numbers are congruent modulo 5?
If x mod 6 = 4, what is (3x) mod 6?
If a is congruent to b modulo n, then a minus b is divisible by n.
Given 100 mod 12 = 4, compute (2 × 100) mod 12 = __
Which property holds for all integers a, b, and positive integer n?
Select all valid congruence statements.
If 8 mod 3 = 2, compute (4 × 8) mod 3.
If A is congruent to B modulo n, then kA is congruent to kB modulo n...
Find the multiplicative inverse of 3 modulo 7.
Solve 7x congruent to 3 modulo 5. What is x modulo 5?
Which linear congruences have exactly one solution modulo m?
Solve 5x ≡ 10 (mod 15). List least residues.
A clock shows 7:00. What time will it show 137 hours later?
Every linear congruence ax ≡ b (mod m) has a solution if gcd(a,m)=1.
Select all true statements about exponent patterns and last digits.
Find the last digit of 13^45.
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