Branch: Number Theory

Number theory is a branch of mathematics dealing with the divisibility properties of integers and in algebraic number fields.

Many problems in number theory can be easily formulated, for instance: What are the integer solutions of a given equation? How many prime numbers are less or equal a given number $n\ge 0$? How many lattice points are there inside a circle/an ellipse? Can every even number be represented as a sum of two prime numbers?

These, and many other number-theoretic questions sound very elementary but turned out to be very hard to answer and many of them have resisted to be answered even until today. However, these hard problems have inspired mathematicians over centuries to develop new ideas and instruments which stimulated even other branches of mathematics.

Theoretical minimum (in a nutshell)

Concepts you will learn in this part of BookofProofs

  1. Part: Historical Development of Number Theory
  2. Part: Elementary Number Theory
  3. Part: Algebraic Number Theory (Link)
  4. Part: Analytic Number Theory
  5. Part: Additive Number Theory
  6. Part: Some Unsolved Number-Theoretic Problems
  7. Part: Solving Strategies and Sample Solutions Related to Number Theory

Parts: 1 2
Persons: 3

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