This set of Discrete Mathematics online quiz focuses on “Quadratic Residue and Pseudo Prime”.

1. If there exist an integer x such that x^{2} ≡ 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 x^{2} ≡ 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) a^{p-1} ≡ 1 (mod p)

b) a^{p-1} ≡ 7 (mod p)

c) a^{p(2)-1} ≡ 1 (mod p)

d) None of the mentioned

View Answer

Explanation: According to Fermat’s little theorem a

^{p-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 x

^{2}≡ 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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