Mathematics · Quantitative Aptitude

Number Theory

438 Questions

Number theory explores the properties and relationships of integers, focusing heavily on prime and composite numbers. Key areas include identifying prime numbers, understanding co primes, and exploring mathematical conjectures like Goldbach's. These questions are a core component of quantitative aptitude sections in banking and government exams.

Prime number identificationCo prime propertiesGoldbach conjectureOdd and even numbersDivisibility rules

Number Theory Questions

Multiple choice

What is R. P. Bambah's most significant contribution to number theory?

  1. Bambah's Prime Number Theorem

  2. Bambah's Goldbach Conjecture

  3. Bambah's Twin Prime Conjecture

  4. Bambah's Fermat's Last Theorem
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

R. P. Bambah's most significant contribution to number theory is Bambah's Prime Number Theorem, which provides an asymptotic formula for the distribution of prime numbers.

Multiple choice

Which of the following is a prime number?

  1. 12

  2. 23

  3. 36

  4. 49
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Out of the given options, only 23 satisfies this condition.

Multiple choice

Determine if 101 is a prime number.

  1. Yes

  2. No
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. 101 is only divisible by 1 and 101, making it a prime number.

Multiple choice

Determine if 1001 is a prime number.

  1. Yes

  2. No
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. 1001 is not a prime number because it is divisible by 7 and 143.

Multiple choice

Which of the following is a property of prime numbers?

  1. They are divisible by 2.

  2. They have exactly two factors.

  3. They are always odd.

  4. They are always even.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself.

Multiple choice

What is the name of the theorem that states that any sufficiently large integer can be expressed as the sum of three primes?

  1. Goldbach's Conjecture

  2. Fermat's Last Theorem

  3. Euler's Theorem

  4. Chinese Remainder Theorem
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Goldbach's Conjecture states that any sufficiently large integer can be expressed as the sum of three primes, but it remains unproven.

Multiple choice

In number theory, what is the name of the theorem that states that every positive integer can be written as a product of prime numbers?

  1. Fundamental Theorem of Arithmetic

  2. Goldbach's Conjecture

  3. Fermat's Last Theorem

  4. Riemann Hypothesis
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Fundamental Theorem of Arithmetic states that every positive integer can be written as a product of prime numbers, and that this factorization is unique up to the order of the factors.

Multiple choice

What is the name of the conjecture that states that every even number greater than 2 can be written as the sum of two primes?

  1. Goldbach's Conjecture

  2. Fermat's Last Theorem

  3. Riemann Hypothesis

  4. P versus NP
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Goldbach's Conjecture states that every even number greater than 2 can be written as the sum of two primes. This conjecture has been proven for all even numbers up to 4³10^{18}, but it remains unproven in general.

Multiple choice

What is the name of the theorem that states that there are infinitely many prime numbers?

  1. Euclid's Theorem

  2. Fermat's Last Theorem

  3. Riemann Hypothesis

  4. P versus NP
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Euclid's Theorem states that there are infinitely many prime numbers. This theorem was first proven by Euclid in his book Elements, and it is one of the most important results in number theory.

Multiple choice

What is the name of the problem that asks whether there exists a polynomial-time algorithm for determining whether a given integer is prime?

  1. Goldbach's Conjecture

  2. Fermat's Last Theorem

  3. Riemann Hypothesis

  4. P versus NP
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The P versus NP problem asks whether there exists a polynomial-time algorithm for determining whether a given integer is prime. This problem is one of the most important unsolved problems in computer science, and it has implications for many areas of computer science, including cryptography, optimization, and artificial intelligence.

Multiple choice

What is the name of the theorem that states that every integer greater than 1 can be written as a product of powers of distinct primes?

  1. Fundamental Theorem of Arithmetic

  2. Goldbach's Conjecture

  3. Fermat's Last Theorem

  4. Riemann Hypothesis
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Fundamental Theorem of Arithmetic states that every integer greater than 1 can be written as a product of powers of distinct primes, and that this factorization is unique up to the order of the factors.

Multiple choice

What is the name of the theorem that states that there are infinitely many twin primes?

  1. Goldbach's Conjecture

  2. Fermat's Last Theorem

  3. Riemann Hypothesis

  4. Hardy–Littlewood conjecture
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Hardy–Littlewood conjecture states that there are infinitely many twin primes, which are pairs of prime numbers that differ by 2.

Multiple choice

What is the name of the theorem that states that the sum of the reciprocals of the primes diverges?

  1. Goldbach's Conjecture

  2. Fermat's Last Theorem

  3. Riemann Hypothesis

  4. Euler's product formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Euler's product formula states that the sum of the reciprocals of the primes diverges.

Multiple choice

What is the name of the theorem that states that every integer greater than 1 can be written as a product of powers of distinct primes?

  1. Goldbach's Conjecture

  2. Fermat's Last Theorem

  3. Riemann Hypothesis

  4. Fundamental Theorem of Arithmetic
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Fundamental Theorem of Arithmetic states that every integer greater than 1 can be written as a product of powers of distinct primes, and that this factorization is unique up to the order of the factors.

Multiple choice

What is the name of the theorem that states that there are infinitely many prime numbers?

  1. Goldbach's Conjecture

  2. Fermat's Last Theorem

  3. Riemann Hypothesis

  4. Euclid's Theorem
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Euclid's Theorem states that there are infinitely many prime numbers. This theorem was first proven by Euclid in his book Elements, and it is one of the most important results in number theory.