Number theory is a branch of pure mathematics which focuses on the positive integers. Number theorists focus on prime numbers and the aspects of objects which are made by integers.
The number theory can be divided into different subcategories which are elementary told, the analytic number theory, the algebraic number theory and the diophantine geometry. However, in the mid-20th century, other approaches and subfield have been developed. These include probabilistic number theory, arithmetic combinatorics and computations in number theory.
Until the mid-20th century, number theory has been considered as the main and purest branch of mathematics, with no direct application to the real world. However, with the computer development, it has been noted how the number theory could give answers to real-world problems as well. Also, computers have enabled number theorists to advance in factoring large numbers and determining primes.
In the context of the number theory, primes and prime factorisation play an important role, as well as functions such as the divisor function, Riemann zeta function and totient function.
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