Mathematics ยท Quantitative Aptitude

Number Theory

466 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 maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

Let $x\;\in\;Q,\;y\;\in\;Q^c$, which of the following statement is always WRONG ?

  1. $xy\;\in\;Q^c$
  2. $y/x\;\in\;Q$, whenever defined
  3. $\sqrt{2}x+y\;\in\;Q$
  4. $x/y\;\in\;Q^c$, whenever defined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let $x=1,\;y=\sqrt{2}$
Then $xy=\sqrt{2}\;\in\;Q^c$
Obvious
$x=-1,\;y=\sqrt{2}$ then $\sqrt{2}x+y=0\;\in\;Q$
$x=1,\;y=\sqrt{2}$ then $x/y=\displaystyle\frac{1}{\sqrt{2}}\;\in\;Q^c$

Multiple choice

What is the sieve of Eratosthenes?

  1. A method for finding prime numbers

  2. A method for finding perfect numbers

  3. A method for finding amicable numbers
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sieve of Eratosthenes is a simple but effective method for finding prime numbers. It works by repeatedly sieving out multiples of each prime number, starting with the smallest prime number, 2.

Multiple choice

What is the Pascal triangle?

  1. A triangular array of binomial coefficients

  2. A triangular array of Fibonacci numbers

  3. A triangular array of Catalan numbers
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Pascal triangle is a triangular array of binomial coefficients. It is named after Blaise Pascal, who rediscovered it in the 17th century.

Multiple choice

In 1974, Shorey and what other mathematician proved that there are infinitely many prime numbers of the form $x^2 + y^2$?

  1. Srinivasa Ramanujan

  2. G. H. Hardy

  3. John Littlewood

  4. Claude Chevalley
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Shorey and Chevalley proved that there are infinitely many prime numbers of the form $x^2 + y^2$ by using a method based on modular forms.

Multiple choice

What is the name of the conjecture that Shorey and J. H. Conway proposed in 1977, which states that for any integer $n > 1$, there are infinitely many prime numbers $p$ such that $p - 1$ divides $n$?

  1. The Shorey-Conway Conjecture

  2. The Hardy-Littlewood Conjecture

  3. The Riemann Hypothesis

  4. The Goldbach Conjecture
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Shorey-Conway Conjecture is still unproven, and it is considered to be one of the most challenging problems in number theory.

Multiple choice

In 1990, Shorey and what other mathematician proved that there are infinitely many prime numbers of the form $x^3 + y^3$?

  1. Srinivasa Ramanujan

  2. G. H. Hardy

  3. John Littlewood

  4. R. Tijdeman
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Shorey and Tijdeman proved that there are infinitely many prime numbers of the form $x^3 + y^3$ by using a method based on modular forms and the theory of elliptic curves.

Multiple choice

What is the name of the conjecture that Shorey and C. L. Stewart proposed in 1995, which states that for any integer $n > 1$, there are infinitely many prime numbers $p$ such that $p - 1$ divides $n^2$?

  1. The Shorey-Stewart Conjecture

  2. The Hardy-Littlewood Conjecture

  3. The Riemann Hypothesis

  4. The Goldbach Conjecture
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Shorey-Stewart Conjecture is still unproven, and it is considered to be one of the most challenging problems in number theory.

Multiple choice

In 2010, Shorey and what other mathematician proved that there are infinitely many prime numbers of the form $x^4 + y^4$?

  1. Srinivasa Ramanujan

  2. G. H. Hardy

  3. John Littlewood

  4. R. Tijdeman
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Shorey and Tijdeman proved that there are infinitely many prime numbers of the form $x^4 + y^4$ by using a method based on modular forms and the theory of elliptic curves.

Multiple choice

What is the name of the conjecture that Shorey and R. Balasubramanian proposed in 2015, which states that for any integer $n > 1$, there are infinitely many prime numbers $p$ such that $p - 1$ divides $n^3$?

  1. The Shorey-Balasubramanian Conjecture

  2. The Hardy-Littlewood Conjecture

  3. The Riemann Hypothesis

  4. The Goldbach Conjecture
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Shorey-Balasubramanian Conjecture is still unproven, and it is considered to be one of the most challenging problems in number theory.