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Number theory is the field of mathematics that is concerned with the properties of numbers, and integers in particular. Number theory can be subdivided in many other fields, according to methods used and the type of questions. The elementary number theory is generally concerned with arithmetic and higher arithmetic terms. Number Theory

Elementary number theory is concerned with the study of integers which are studied without use of techniques from other mathematical fields. Questions of divisibility, integer factorizations into prime numbers, use of the Euclidean algorithm to compute greatest common divisors, investigation of perfect numbers or congruences. Many important discoveries of this math field are Fermat's little theorem, the Chinese remainder theorem, Euler's theorem and the law of quadratic reciprocity. The properties of multiplicative functions for example Möbius function or Euler's φ function, factorials, integer sequences and Fibonacci numbers all also covered into this area.

Main Fields of Number Theory

1. Analytic Number Theory
2. Algebraic number Theory
3. Geometry of numbers
4. Combinatorial number theory
5. Arithmetic algebraic geometry
6. Arithmetic topology
7. Modular forms