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."

數論（英語： Number theory ）是纯粹数学的分支之一，主要研究整数的性質，被稱為「最純」的數學領域。

数论（number theory），是 纯粹数学 的分支之一，主要研究 整数 的性质。 整数可以是方程式的解（丢番图方程）。 有些 解析函数 （像 黎曼ζ函数）中包括了一些整数、质数的性质，透过这些函数也可以了解一些数论的问题。 透过数论也可以建立实数和有理数之间的关系，并且用有理数来逼近实数（丢番图逼近）。 按研究方法来看，数论大致可分为 初等数论 和高等数论。 初等数论是用初等方法研究的数论，它的研究方法本质上说，就是利用整数环的整除性质，主要包括整除 …

This 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.

2025年1月20日 · Number theory is a branch of mathematics that studies numbers, particularly whole numbers, and their properties and relationships. It explores patterns, structures, and the behaviours of numbers in different situations.

The main goal of number theory is to discover interesting and unexpected rela-tionships between different sorts of numbers and to prove that these relationships are true.

2025年1月31日 · Number theory, branch of mathematics concerned with properties of the positive integers (1, 2, 3, …). Modern number theory is a broad subject that is classified into subheadings such as elementary number theory, algebraic number theory, analytic number theory, and geometric 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. Since you've been dealing with whole numbers of one kind or another for almost your whole life, some of what we'll see in the text will seem familiar, and much may ...

Number theory has applications in computer science due to connections with cryptography. The research interests of our group include Galois representations, Shimura varieties, automorphic forms, lattices, algorithmic aspects, rational points on varieties, and the arithmetic of K3 surfaces.

This is Number theory, a branch of mathematics that explores the properties and relationships of integers. The cool part is that anyone can join in; it is mostly basic operations like multiplication and addition!