Number theory is one of the oldest branches of mathematics alongside geometry. One quirk of number theory is that it deals with statements that are simple to understand but are very difficult to solve.

number theory, branch of mathematics concerned with properties of the positive integers (1, 2, 3, …). Sometimes called “higher arithmetic,” it is among the oldest and most natural of mathematical pursuits.

By considering each case we see that the number of elements greater than p/2 is even when p = 1,7 (mod 8) and odd when p = 3,5 (mod 8). We restate this as follows.

The Riemann hypothesis, a Clay Millennium Problem, is a part of analytic number theory, which employs analytic methods (calculus and complex analysis) to understand the integers.

Student Guides to Number Theory Introductory topics in number theory Covers different kinds of integers such as prime numbers, composite numbers, perfect squares and their relationships …

We only have integers, which are whole numbers, their negatives, and zero: This is Number theory, a branch of mathematics that explores the properties and relationships of integers. The cool part is that …

Sep 19, 2025 · Number theory is a branch of mathematics that studies numbers, particularly whole numbers, and their properties and relationships. It explores patterns, structures, and the behaviors of …

3 days ago · Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and prime …

Number theory is one of the oldest branches of mathematics and is concerned with the properties of numbers in general. In the past few decades, research in number theory has progressed at a rapid …

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.