# Discrete Mathematics Questions and Answers – Number Theory – Quadratic Residue and Pseudo Prime

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

1. If there exist an integer x such that x2 ≡ q (mod n). then q is called ______________
b) Linear Residue
c) Pseudoprime
d) None of the mentioned

Explanation: q is called quadratic residue if it is congruent to a perfect square modulo n.

2. If there exist no integer x such that x2 ≡ q (mod n). then q is called __________
c) Pseudoprime
d) None of the mentioned

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

Explanation: According to Fermat’s little theorem ap-1 ≡ 1 (mod p).

4. 5 is quardratic non-residue of 7.
a) True
b) False

Explanation: Since there exists no number which gives 5 modulo 7 when squared.

5. 4 is quardratic residue of 7.
a) True
b) False

Explanation: Since 25 ≡ 4(mod)7, 4 is quardratic residue of 7.
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6. 8 is quardratic residue of 17.
a) True
b) False

Explanation: Since 25 ≡ 8(mod)17.

7. 8 is quardratic residue of 11.
a) True
b) False

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

Explanation: Since 4, 16, 32 satisfies the criteria, all are quardratic residue of 11.

9. What is pseudo prime number?
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

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

Explanation: Fermat pseudoprime, Fibonacci pseudoprime, Euler pseudoprime are different classes of pseudoprimes.

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