1. Calculate the GCD of 8376238 and 1921023 using Euclidean algorithm.
a) 13
b) 12
c) 17
d) 7
Explanation: GCD(8376238, 1921023) = 13.
2. What is 11 mod 7 and -11 mod 7?
a) 4 and 5
b) 4 and 4
c) 5 and 3
d) 4 and -4
Explanation: 11 mod 7 = 4 ; -11 mod 7 = -4 mod 7 = 3 mod 7.
3. Which of the following is a valid property for concurrency?
a) a = b (mod n) if n|(a-b)
b) a = b (mod n) implies b = a (mod n)
c) a = b (mod n) and b = c (mod n) implies a = c (mod n)
d) All of the mentioned
Explanation: All are valid properties of congruences and can be checked by using substituting values.
4. [(a mod n) + (b mod n)] mod n = (a+b) mod n
a) True
b) False
Explanation: The equivalence is true and can be checked by substituting values.
5. [(a mod n) – (b mod n)] mod n = (b – a) mod n
a) True
b) False
Explanation: The equivalence is false and can be checked by substituting values. The correct equivalence would be [(a mod n) – (b mod n)] mod n = (a – b) mod n.
6. 117 mod 13 =
a) 3
b) 7
c) 5
d) 15
Explanation: The correct answer is 2. Or in this case 15 mod 13 = 2.
7. The multiplicative Inverse of 1234 mod 4321 is
a) 3239
b) 3213
c) 3242
d) Does not exist
Explanation: The multiplicative Inverse of 1234 mod 4321 is 3239.
8. The multiplicative Inverse of 550 mod 1769 is
a) 434
b) 224
c) 550
d) Does not exist
Explanation: The multiplicative Inverse of 550 mod 1769 is 550.
9. The multiplicative Inverse of 24140 mod 40902 is
a) 2355
b) 5343
c) 3534
d) Does not exist
Explanation: The multiplicative Inverse does not exist as GCD (24140, 40902) = 34.
10. A very common field in this category is GF(2) with the set {1, 2} and two operations, addition and multiplication.
a) True
b) False
Explanation: GF(2) is the set {0, 1} with two operations, addition and multiplication