Number Theory MCQs With Answers

Computer MCQs 360July 14, 2023

0 8 1 minute read

Welcome to the Number Theory MCQs with Answers. In this post, we have shared Number Theory Online Test for different competitive exams. Find practice Number Theory Practice Questions with answers in Computer Tests exams here. Each question offers a chance to enhance your knowledge regarding Number Theory.

Number Theory MCQs

By presenting 3 options to choose from, Number Theory Quiz which cover a wide range of topics and levels of difficulty, making them adaptable to various learning objectives and preferences. You will have to read all the given answers of Number Theory Questions and Answers and click over the correct answer.

Test Name: Number Theory MCQ Quiz Practice
Type: Quiz Test
Total Questions: 40
Total Marks: 40
Time: 40 minutes

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Number Theory

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1 / 40

Which prime number is the only even prime?

2 / 40

What is the time complexity of the Miller-Rabin algorithm?

O(n log n)

O(k log n)

O(n^2)

3 / 40

What is a quadratic residue modulo n?

An integer divisible by n

A prime number

An integer that is a square modulo n

4 / 40

Which number is known as the multiplicative inverse of 5 modulo 7?

5 / 40

What is the main application of the RSA algorithm?

Finding prime numbers

Solving linear congruences

Public-key cryptography

6 / 40

What is the characteristic property of a perfect square?

It is even

It is prime

It can be expressed as the product of an integer with itself

7 / 40

What is Fermat's Little Theorem used for?

Finding the GCD

Factoring large numbers

Finding powers of integers modulo a prime

8 / 40

Which algorithm is used to find the modular multiplicative inverse?

Sieve of Eratosthenes

Extended Euclidean Algorithm

Fermat's Little Theorem

9 / 40

Which number is both a triangular and a square number?

10 / 40

What is a Carmichael number?

A number that has no prime factors

A prime number

A composite number that satisfies Fermat's Little Theorem for all integers

11 / 40

What is the time complexity of the Sieve of Eratosthenes?

O(n log n)

O(n log log n)

O(n^2)

12 / 40

What is the main application of the Sieve of Eratosthenes?

Finding the GCD

Computing modular inverses

Finding all prime numbers up to a given limit

13 / 40

What is the main use of the Legendre symbol?

Computing GCD

Determining quadratic residues

Finding prime numbers

14 / 40

What does it mean for two numbers to be coprime?

Their GCD is 1

Their sum is a prime number

They are both prime

15 / 40

What does Wilson's Theorem state?

Every prime is of the form 6k±1

(p-1)! ≡ -1 (mod p) if p is prime

p is a product of primes

16 / 40

Which number is known as the additive identity?

-1

17 / 40

What is the time complexity of the Euclidean algorithm?

O(log(min(a, b)))

O(n^2)

O(n)

18 / 40

What is the value of φ(p) where p is a prime number?

p - 1

19 / 40

What is the main purpose of modular arithmetic?

Solving quadratic equations

Finding prime numbers

Handling computations with integers where overflow can occur

20 / 40

What is a perfect number?

A number equal to the sum of its proper divisors

A number with no divisors

A prime number

21 / 40

What is a Mersenne prime?

A prime of the form p^2 - 1

A prime of the form 2p + 1

A prime of the form 2^p - 1 where p is prime

22 / 40

What is the first perfect number?

496

23 / 40

What is the Euclidean algorithm used for?

Finding prime numbers

Finding the least common multiple (LCM)

Finding the greatest common divisor (GCD)

24 / 40

What is the largest known prime number used in cryptography?

A Mersenne prime

A Wilson prime

A Gaussian prime

25 / 40

Which number is known as the multiplicative identity?

-1

26 / 40

What is a primitive root modulo n?

An integer whose powers modulo n generate all integers relatively prime to n

A factor of n

A prime number

27 / 40

Which theorem allows us to solve systems of simultaneous congruences with different moduli?

Chinese Remainder Theorem

Fundamental Theorem of Arithmetic

Fermat's Little Theorem

28 / 40

Which theorem generalizes Fermat's Little Theorem?

Wilson's Theorem

Chinese Remainder Theorem

Euler's Theorem

29 / 40

What is the main purpose of the Totient Function in RSA?

Compute modular inverses

Determine the public and private keys

Factorize large numbers

30 / 40

Which number is known as the additive inverse of 3 modulo 7?

31 / 40

What is the time complexity of the Exponentiation by Squaring algorithm?

O(n log n)

O(log n)

O(n)

32 / 40

What is a Gaussian integer?

A complex number where both real and imaginary parts are integers

An integer divisible by a prime

A rational number

33 / 40

Which algorithm is used for fast exponentiation?

Extended Euclidean Algorithm

Exponentiation by Squaring

Euclidean Algorithm

34 / 40

What is the value of 7^0 in modular arithmetic?

35 / 40

Which theorem states that there are infinitely many primes?

Fermat's Little Theorem

Euclid's theorem

Wilson's Theorem

36 / 40

What is the purpose of the Miller-Rabin algorithm?

Factoring integers

Primality testing

Computing modular inverses

37 / 40

What is the value of φ(10) in Euler's Totient Function?

38 / 40

Which theorem states that every integer greater than 1 is either a prime or a product of primes?

Fundamental Theorem of Arithmetic

Fermat's Little Theorem

Chinese Remainder Theorem

39 / 40

What is the time complexity of the Extended Euclidean Algorithm?

O(log n)

O(n^2)

O(n log n)

40 / 40

What is Euler's Totient Function used for?

Counting integers relatively prime to n

Finding prime numbers

Solving linear congruences

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Computer MCQs 360July 14, 2023

0 8 1 minute read