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Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."
Download as PDF; Printable version; In other projects ... This is a list of algebraic number theory topics. Basic topics. These topics are basic to the field, either ...
Download as PDF; Printable version; In other projects Wikidata item; ... This is a list of topics in number theory. See also: List of recreational number theory topics;
Basic Number Theory is an influential book [1] by André Weil, an exposition of algebraic number theory and class field theory with particular emphasis on valuation-theoretic methods. Based in part on a course taught at Princeton University in 1961–62, it appeared as Volume 144 in Springer's Grundlehren der mathematischen Wissenschaften ...
A subset A of positive integers has natural density α if the proportion of elements of A among all natural numbers from 1 to n converges to α as n tends to infinity.. More explicitly, if one defines for any natural number n the counting function a(n) as the number of elements of A less than or equal to n, then the natural density of A being α exactly means that [1]
Its authors have divided Elementary Number Theory, Group Theory and Ramanujan Graphs into four chapters. The first of these provides background in graph theory, including material on the girth of graphs (the length of the shortest cycle), on graph coloring, and on the use of the probabilistic method to prove the existence of graphs for which both the girth and the number of colors needed are ...
1. The class number of a number field is the cardinality of the ideal class group of the field. 2. In group theory, the class number is the number of conjugacy classes of a group. 3. Class number is the number of equivalence classes of binary quadratic forms of a given discriminant. 4. The class number problem. conductor
Traditionally, number theory is the branch of mathematics concerned with the properties of integers and many of its open problems are easily understood even by non-mathematicians. More generally, the field has come to be concerned with a wider class of problems that arise naturally from the study of integers.