Number Theory Quiz 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

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

2 / 40

Which algorithm is used to find the modular multiplicative inverse?

Fermat's Little Theorem

Extended Euclidean Algorithm

Sieve of Eratosthenes

3 / 40

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

4 / 40

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

5 / 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

6 / 40

What is the time complexity of the Extended Euclidean Algorithm?

O(n log n)

O(log n)

O(n^2)

7 / 40

What is the main purpose of modular arithmetic?

Handling computations with integers where overflow can occur

Solving quadratic equations

Finding prime numbers

8 / 40

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

Fermat's Little Theorem

Fundamental Theorem of Arithmetic

Chinese Remainder Theorem

9 / 40

What is a Mersenne prime?

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

A prime of the form 2p + 1

A prime of the form p^2 - 1

10 / 40

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

11 / 40

What is Euler's Totient Function used for?

Counting integers relatively prime to n

Solving linear congruences

Finding prime numbers

12 / 40

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

Determine the public and private keys

Compute modular inverses

Factorize large numbers

13 / 40

What is the first perfect number?

496

14 / 40

Which theorem states that there are infinitely many primes?

Euclid's theorem

Fermat's Little Theorem

Wilson's Theorem

15 / 40

What is the main use of the Legendre symbol?

Finding prime numbers

Computing GCD

Determining quadratic residues

16 / 40

What is the characteristic property of a perfect square?

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

It is prime

It is even

17 / 40

What is Fermat's Little Theorem used for?

Finding powers of integers modulo a prime

Finding the GCD

Factoring large numbers

18 / 40

What is the main application of the Sieve of Eratosthenes?

Finding all prime numbers up to a given limit

Finding the GCD

Computing modular inverses

19 / 40

What is a perfect number?

A number equal to the sum of its proper divisors

A number with no divisors

A prime number

20 / 40

Which algorithm is used for fast exponentiation?

Exponentiation by Squaring

Extended Euclidean Algorithm

Euclidean Algorithm

21 / 40

What is the main application of the RSA algorithm?

Solving linear congruences

Finding prime numbers

Public-key cryptography

22 / 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

23 / 40

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

24 / 40

Which number is both a triangular and a square number?

25 / 40

What does Wilson's Theorem state?

p is a product of primes

Every prime is of the form 6k±1

(p-1)! ≡ -1 (mod p) if p is prime

26 / 40

Which theorem generalizes Fermat's Little Theorem?

Wilson's Theorem

Chinese Remainder Theorem

Euler's Theorem

27 / 40

What is the time complexity of the Sieve of Eratosthenes?

O(n^2)

O(n log log n)

O(n log n)

28 / 40

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

O(n)

O(log n)

O(n log n)

29 / 40

What is the largest known prime number used in cryptography?

A Mersenne prime

A Wilson prime

A Gaussian prime

30 / 40

What is a Gaussian integer?

An integer divisible by a prime

A complex number where both real and imaginary parts are integers

A rational number

31 / 40

Which number is known as the additive identity?

-1

32 / 40

What is a quadratic residue modulo n?

An integer divisible by n

An integer that is a square modulo n

A prime number

33 / 40

What is a Carmichael number?

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

A number that has no prime factors

A prime number

34 / 40

Which prime number is the only even prime?

35 / 40

What is the purpose of the Miller-Rabin algorithm?

Primality testing

Computing modular inverses

Factoring integers

36 / 40

Which number is known as the multiplicative identity?

-1

37 / 40

What is the Euclidean algorithm used for?

Finding the greatest common divisor (GCD)

Finding prime numbers

Finding the least common multiple (LCM)

38 / 40

What is the time complexity of the Euclidean algorithm?

O(n^2)

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

O(n)

39 / 40

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

p - 1

40 / 40

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

O(k log n)

O(n^2)

O(n log n)

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Computer MCQs 360July 14, 2023

0 8 1 minute read