This set of Discrete Mathematics online quiz focuses on “Quadratic Residue and Pseudo Prime”.
1. If there exist an integer x such that x2 ≡ q (mod n). then q is called:
a) Quadratic Residue
b) Linear Residue
c) Pseudoprime
d) None of the mentioned
View Answer
Explanation: q is called quadratic residue if it is congurent to a perfect square modulo n.
2. If there exist no integer x such that x2 ≡ q (mod n). then q is called:
a) Quadratic Residue
b) Quadratic Nonresidue
c) Pseudoprime
d) None of the mentioned
View Answer
Explanation: q is called quadratic nonresidue if it is not congurent to a perfect square modulo n.
3. The Fermat’s little theorem for odd prime p and coprime number a,is:
a) ap-1 ≡ 1 (mod p)
b) ap-1 ≡ 7 (mod p)
c) ap(2)-1 ≡ 1 (mod p)
d) None of the mentioned
View Answer
Explanation: According to Fermat’s little theorem ap-1 ≡ 1 (mod p).
4. State whether the given statement is true or false
5 is quardratic non-residue of 7.
a) True
b) False
View Answer
Explanation: Since there exist no number which gives 5 modullo 7 when squared.
5. State whether the given statement is true or false
4 is quardratic residue of 7.
a) True
b) False
View Answer
Explanation: Since 25 ≡ 4(mod)7 , 4 is quardratic residue of 7.
6. State whether the given statement is true or false
8 is quardratic residue of 17.
a) True
b) False
View Answer
Explanation: Since 25 ≡ 8(mod)17.
7. State whether the given statement is true or false
8 is quardratic residue of 11 .
a) True
b) False
View Answer
Explanation: Since x2 ≡ 8(mod)17 has no solutions.
8. Which of the following is a quardratic residue of 11?
a) 4
b) 5
c) 9
d) All of the mentioned
View Answer
Explanation: Since 4, 16, 32 satisfies the criteria, all are quardratic residue of 11.
9. A pseudo prime number is
a) is a probable prime and is not a prime number
b) is a prime number
c) does not share any property with prime number
d) none of the mentioned
View Answer
Explanation: A pseudo prime number is an integer that shares a property common to all prime number and is not a prime number.
10. Pseudo prime are classified based on property which they satisfy,which of the following are classes of pseudoprimes:
a) Fermat pseudoprime
b) Fibonacci pseudoprime
c) Euler pseudoprime
d) All of the mentioned
View Answer
Explanation: Fermat pseudoprime, Fibonacci pseudoprime, Euler pseudoprime are differnet classes of pseudoprimes.
Sanfoundry Global Education & Learning Series – Discrete Mathematics.
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