Applied Maths - Congruence Modulo

Grade 12 Maths — Applied Maths - Congruence Modulo: 25 practice questions with instant scoring and explanations.

1. Two numbers are congruent modulo m if their difference is divisible by:
2. The properties of congruence include:
3. If a ≡ b (mod m), then b ≡ a (mod m) is the _______ property:
4. If a ≡ b (mod m) and b ≡ c (mod m), then a ≡ c (mod m) is:
5. Congruence modulo m forms an:
6. For congruence modulo 5, the equivalence classes are:
7. The set of all residue classes modulo m is denoted:
8. In ℤ_m, the addition is well-defined, meaning if a ≡ a' and b ≡ b' (mod m), then:
9. The complete residue system modulo 6 is:
10. A reduced residue system modulo 8 contains:
11. The number of elements in a reduced residue system modulo m is:
12. Cancellation property: if ac ≡ bc (mod m) and gcd(c,m) = 1, then:
13. The sum of a complete residue system modulo m equals:
14. If p is prime, then the only solutions to x² ≡ 1 (mod p) are:
15. The quadratic residue theorem deals with:
16. An integer a is a quadratic residue modulo p if:
17. The Legendre symbol (a/p) = 1 if:
18. The law of quadratic reciprocity relates:
19. The order of an element a in (ℤ_p)* is:
20. A primitive root modulo p is:
21. For prime p, the group (ℤ_p, ×) is:
22. The structure of ℤ_p* (multiplicative group) with p prime is:
23. a ≡ b (mod n) means:
24. 17 ≡ ? (mod 6):
25. If a ≡ b (mod m) and c ≡ d (mod m), then a + c ≡ ? (mod m):