Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. It is sometimes called "The Queen of Mathematics" because of its foundational place in the discipline.

What is Number Theory?

Number theory is the study of numbers, their properties, and their applications. It is a vast field that includes many different topics, such as:

  • Prime Numbers: Numbers that are only divisible by 1 and themselves.
  • Fermat's Last Theorem: A theorem that states that no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2.
  • Modular Arithmetic: A system of arithmetic for integers, where numbers "wrap around" after reaching a certain value.

Interesting Facts

  • The number 2 is the only even prime number.
  • The number 17 is the only number that is both a square and a cube (17 = 4^2 = 2^3).
  • The number 0 is neither positive nor negative.

Resources

For more information on number theory, you can visit our Number Theory page.

Prime Numbers

Prime numbers are fundamental in number theory. Here are a few prime numbers:

  • 2
  • 3
  • 5
  • 7
  • 11
  • 13
  • 17
  • 19
  • 23
  • 29

Prime Number Theorem

The Prime Number Theorem states that the number of primes less than a given number n is approximately n/ln(n).

Mathematical Formula

The most famous formula in number theory is Euler's formula:

[ e^{i\pi} + 1 = 0 ]

This formula connects five fundamental mathematical constants: e, i, π, 1, and 0.

Here's a beautiful image of a prime number pattern:

Prime Number Pattern