WEBCarl Friedrich Gauss. Number theory, known to Gauss as “arithmetic,” studies the properties of the integers: . . . − 3, −2, −1, 0, 1, 2, 3 . . . . Although the integers are familiar, and their properties might therefore seem simple, it is instead a very deep subject.
WEBWe then introduce the elementary but fundamental concept of a greatest common divisor (gcd) of two integers, and the Euclidean algorithm for finding the gcd of two integers.
1.1: What Is Number Theory? - Mathematics LibreTexts
WEBSo what is "arithmetic," or number theory? Simply stated, number theory is concerned with questions about and properties of the integers \[\dots, -4, -3, -2, -1, 0, 1, 2, 3, 4, \dots\nonumber \] and closely-related numbers.
Theory of Numbers | Mathematics | MIT OpenCourseWare
WEBThis course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.
Number theory - Wikipedia
WEBElementary number theory is taught in discrete mathematics courses for computer scientists; on the other hand, number theory also has applications to the continuous in numerical analysis. [90] Number theory has now several modern applications spanning diverse areas such as:
1.4: Definitions of Elementary Number Theory - Mathematics ...
WEBIn this section, we discuss some basic definitions of terms related to the elementary number theory, including even and odd, decimal and Base-n notation, divisibility, floor and ceilings, div and mod,…
Elementary Number Theory - SpringerLink
WEBOverview. Authors: Gareth A. Jones, J. Mary Jones. The essential guide to number theory for undergraduates. Distinguishing features include discussions of the Riemann Zeta Function and Riemann Hypothesis. Includes supplementary material: sn.pub/extras.
An Introduction to the Theory of Numbers - Open Textbook Library
WEBTopics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers.
Elementary Number Theory -- from Wolfram MathWorld
WEBAug 22, 2024 · Elementary number theory is the branch of number theory in which elementary methods (i.e., arithmetic, geometry, and high school algebra) are used to solve equations with integer or rational solutions.
WEBThis course will be an introduction to elementary number theory. The word “elementary” here has a technical meaning: it indicates that we won’t be using more advanced theories (such as complex analysis or algebraic geometry) to study number-theoretical patterns.