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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.
Proven to be impossible to prove or disprove within Zermelo–Fraenkel set theory with or without the axiom of choice (provided Zermelo–Fraenkel set theory is consistent, i.e., it does not contain a contradiction). There is no consensus on whether this is a solution to the problem. 1940, 1963 2nd
This problem can be found amongst the problems proposed by Paul Erdős in combinatorial number theory, known by English speakers as the Minimum overlap problem.It was first formulated in the 1955 article Some remarks on number theory [3] (in Hebrew) in Riveon Lematematica, and has become one of the classical problems described by Richard K. Guy in his book Unsolved problems in number theory.
List of unsolved problems may refer to several notable conjectures or open problems in various academic fields: Natural sciences, engineering and medicine [ edit ]
Szemerédi's theorem states that a set of natural numbers of non-zero upper asymptotic density contains finite arithmetic progressions, of any arbitrary length k. Erdős made a more general conjecture from which it would follow that The sequence of primes numbers contains arithmetic progressions of any length.
The other six Millennium Prize Problems remain unsolved, despite a large number of unsatisfactory proofs by both amateur and professional mathematicians. Andrew Wiles , as part of the Clay Institute's scientific advisory board, hoped that the choice of US$ 1 million prize money would popularize, among general audiences, both the selected ...
An intersecting family of -element sets may be maximal, in that no further set can be added (even by extending the ground set) without destroying the intersection property, but not of maximum size. An example with n = 7 {\displaystyle n=7} and r = 3 {\displaystyle r=3} is the set of seven lines of the Fano plane , much less than the Erdős–Ko ...
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.
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