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

What is the time complexity of the Euclidean algorithm?

O(n)

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

O(n^2)

2 / 40

Which algorithm is used to find the modular multiplicative inverse?

Sieve of Eratosthenes

Fermat's Little Theorem

Extended Euclidean Algorithm

3 / 40

What is a Carmichael number?

A prime number

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

A number that has no prime factors

4 / 40

Which number is both a triangular and a square number?

5 / 40

What is a perfect number?

A prime number

A number equal to the sum of its proper divisors

A number with no divisors

6 / 40

Which algorithm is used for fast exponentiation?

Euclidean Algorithm

Exponentiation by Squaring

Extended Euclidean Algorithm

7 / 40

What is the main use of the Legendre symbol?

Finding prime numbers

Computing GCD

Determining quadratic residues

8 / 40

What is the time complexity of the Sieve of Eratosthenes?

O(n log n)

O(n log log n)

O(n^2)

9 / 40

What is the time complexity of the Extended Euclidean Algorithm?

O(log n)

O(n^2)

O(n log n)

10 / 40

Which theorem generalizes Fermat's Little Theorem?

Euler's Theorem

Wilson's Theorem

Chinese Remainder Theorem

11 / 40

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

12 / 40

What is the first perfect number?

496

13 / 40

What does it mean for two numbers to be coprime?

Their GCD is 1

They are both prime

Their sum is a prime number

14 / 40

What is Euler's Totient Function used for?

Counting integers relatively prime to n

Finding prime numbers

Solving linear congruences

15 / 40

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

16 / 40

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

Chinese Remainder Theorem

Fermat's Little Theorem

Fundamental Theorem of Arithmetic

17 / 40

What is Fermat's Little Theorem used for?

Finding powers of integers modulo a prime

Factoring large numbers

Finding the GCD

18 / 40

Which number is known as the additive identity?

-1

19 / 40

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

p - 1

20 / 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

21 / 40

What is the main application of the Sieve of Eratosthenes?

Finding all prime numbers up to a given limit

Computing modular inverses

Finding the GCD

22 / 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

23 / 40

What is a primitive root modulo n?

A factor of n

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

A prime number

24 / 40

What is a quadratic residue modulo n?

A prime number

An integer divisible by n

An integer that is a square modulo n

25 / 40

What is the main purpose of modular arithmetic?

Solving quadratic equations

Handling computations with integers where overflow can occur

Finding prime numbers

26 / 40

What is the purpose of the Miller-Rabin algorithm?

Factoring integers

Computing modular inverses

Primality testing

27 / 40

Which prime number is the only even prime?

28 / 40

What is a Gaussian integer?

An integer divisible by a prime

A rational number

A complex number where both real and imaginary parts are integers

29 / 40

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

O(n log n)

O(n^2)

O(k log n)

30 / 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

31 / 40

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

O(log n)

O(n log n)

O(n)

32 / 40

Which number is known as the multiplicative identity?

-1

33 / 40

What is the main application of the RSA algorithm?

Solving linear congruences

Public-key cryptography

Finding prime numbers

34 / 40

What is the Euclidean algorithm used for?

Finding prime numbers

Finding the least common multiple (LCM)

Finding the greatest common divisor (GCD)

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 largest known prime number used in cryptography?

A Gaussian prime

A Wilson prime

A Mersenne prime

37 / 40

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

Compute modular inverses

Factorize large numbers

Determine the public and private keys

38 / 40

What does Wilson's Theorem state?

p is a product of primes

(p-1)! ≡ -1 (mod p) if p is prime

Every prime is of the form 6k±1

39 / 40

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

40 / 40

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

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Computer MCQs 360July 14, 2023

0 8 1 minute read