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.

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 …

4 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 …

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 …

Karl-Dieter Crisman 's Number Theory: In Context and Interactive is a free textbook for an upper-level (US) number theory course, with a clear vision to expose students to the connections to all areas of …

Take a guided, problem-solving based approach to learning Number Theory. These compilations provide unique perspectives and applications you won't find anywhere else.

0 Preface This set of notes on number theory was originally written in 1995 for students at the IMO level. It covers the basic background material that an IMO student should be familiar with. This text is …