Applied Maths - Modulo Arithmetic

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

1. a ≡ b (mod m) means:
2. 15 ≡ ? (mod 7)
3. The remainder when 47 is divided by 11 is:
4. If a ≡ b (mod m) and c ≡ d (mod m), then a + c ≡ :
5. If a ≡ b (mod m), then ac ≡ :
6. The additive identity in modulo m arithmetic is:
7. The multiplicative identity in modulo m arithmetic is:
8. 17 + 19 ≡ ? (mod 12)
9. 5 × 8 ≡ ? (mod 7)
10. The inverse of 3 modulo 7 is:
11. Fermat's Little Theorem states: if p is prime and gcd(a,p) = 1, then a^(p−1) ≡ :
12. 3^4 ≡ ? (mod 5)
13. The linear congruence 2x ≡ 5 (mod 7) has solution:
14. A linear congruence ax ≡ b (mod m) has a solution iff:
15. 2^10 ≡ ? (mod 11)
16. The Chinese Remainder Theorem applies when moduli are:
17. x ≡ 2 (mod 3) and x ≡ 3 (mod 5) have solution:
18. The order of a modulo m is the smallest positive integer k such that:
19. gcd(12, 18) ≡ ?
20. If a ≡ b (mod m) and c ≡ d (mod m), then a × c ≡ ?
21. The multiplicative inverse of a modulo m exists iff:
22. Euler's theorem states: if gcd(a,m) = 1, then a^φ(m) ≡ :
23. φ(6) (Euler's totient) = :
24. Question?
25. Question?