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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Pages in category "Unsolved problems in number theory" The following 106 pages are in this category, out of 106 total. This list may not reflect recent changes. A.
Bernoulli number. Agoh–Giuga conjecture; Von Staudt–Clausen theorem; Dirichlet series; Euler product; Prime number theorem. Prime-counting function. Meissel–Lehmer algorithm; Offset logarithmic integral; Legendre's constant; Skewes' number; Bertrand's postulate. Proof of Bertrand's postulate; Proof that the sum of the reciprocals of the ...
The Ages of Three Children puzzle (sometimes referred to as the Census-Taker Problem [1]) is a logical puzzle in number theory which on first inspection seems to have insufficient information to solve. However, with closer examination and persistence by the solver, the question reveals its hidden mathematical clues, especially when the solver ...
One may ask analytic questions about algebraic numbers, and use analytic means to answer such questions; it is thus that algebraic and analytic number theory intersect. For example, one may define prime ideals (generalizations of prime numbers in the field of algebraic numbers) and ask how many prime ideals there are up to a certain size.
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.
This is a list of recreational number theory topics (see number theory, recreational mathematics). Listing here is not pejorative : many famous topics in number theory have origins in challenging problems posed purely for their own sake.
The Erdős–Straus conjecture is an unproven statement in number theory. The conjecture is that, for every integer n {\displaystyle n} that is greater than or equal to 2, there exist positive integers x {\displaystyle x} , y {\displaystyle y} , and z {\displaystyle z} for which 4 n = 1 x + 1 y + 1 z . {\displaystyle {\frac {4}{n}}={\frac {1}{x ...
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