Elementary Number Theory

Divisibility, congruences, arithmetic functions, and basic primes.

foundation tier

Elementary Number Theory. Divisibility, congruences, arithmetic functions, and basic primes. This page collects canonical references that organise the subject and provide entry points to its main techniques.

Foundations and canonical references

The standard treatments of elementary number theory approach the subject from complementary angles. Niven, An Introduction to the Theory of Numbers (1991) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Rosen, Elementary Number Theory (2010) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.

Open methodological questions for elementary number theory include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 1991
    An Introduction to the Theory of Numbers
    niven-1991, zuckerman-1991, montgomery-1991
  • textbook · primary · 2010
    Elementary Number Theory
    rosen-kenneth-2010

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Explore

  1. 01

    Modular Arithmetic

    Congruences, Fermat–Euler, CRT, and primitive roots.
  2. 02

    Arithmetic Functions

    Multiplicative functions, Möbius inversion, and Dirichlet convolution.

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