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Number Theory

Number theory, as the name suggests, is the study of the properties and relationships of integers and has a long history dating back to the very inception of mathematics. Gauss famously said about number theory:

“Mathematics is the queen of sciences, and number theory is the queen of mathematics.”

Elementary Number Theory

The term “elementary” in this context contrasts with analytic or algebraic number theory and does not imply simplicity at the level of elementary school. While understanding the propositions may be relatively straightforward, the field itself is not inherently simple. Many mathematically talented individuals are introduced to number theory from a young age.

Multiples and Divisors

Primes

Modular Arithmetic

Perfect Numbers

Quadratic Reciprocity

Elliptic Curves

Cryptography

Initially, cryptography was a prominent application of number theory. For thousands of years, number theory, once purely a branch of pure mathematics, transformed into a practical field through applications in cryptography, and recently, abstract algebra has been applied.

Discrete Logarithms

Factorization

Algebraic Number Theory

Extended Rings

Analytic Number Theory

Arithmetic Functions

References

  • Silverman. (2012). A Friendly Introduction to Number Theory (4th Edition)
  • Apostol. (1976). Introduction to Analytic Number Theory
  • Hoffstein. (2008). An Introduction to Mathematical Cryptography

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