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Diophantus II.IX reaches the same solution by an even quicker route which is very similar to the 'generalized solution' above. Once again the problem is to divide 16 into two squares. [3] Let the first number be N and the second an arbitrary multiple of N diminished by the root (of) 16. For example 2N − 4. Then:
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.
Finding the global minimum solution of a Hartree-Fock problem [37] Upward planarity testing [8] Hospitals-and-residents problem with couples; Knot genus [38] Latin square completion (the problem of determining if a partially filled square can be completed) Maximum 2-satisfiability [3]: LO5
Whether these problems are not decidable in polynomial time is one of the greatest open questions in computer science (see P versus NP ("P = NP") problem for an in-depth discussion). An important notion in this context is the set of NP-complete decision problems, which is a subset of NP and might be informally described as the "hardest ...
Hilbert's eighth problem is one of David Hilbert's list of open mathematical problems posed in 1900. It concerns number theory , and in particular the Riemann hypothesis , [ 1 ] although it is also concerned with the Goldbach conjecture .
Archimedes's cattle problem (or the problema bovinum or problema Archimedis) is a problem in Diophantine analysis, the study of polynomial equations with integer solutions. Attributed to Archimedes , the problem involves computing the number of cattle in a herd of the sun god from a given set of restrictions.
The origin of the Entscheidungsproblem goes back to Gottfried Leibniz, who in the seventeenth century, after having constructed a successful mechanical calculating machine, dreamt of building a machine that could manipulate symbols in order to determine the truth values of mathematical statements. [3]
Uzquiano (2010) uses these techniques to provide a two question solution to the amended puzzle. [9] [10] Two question solutions to both the original and amended puzzle take advantage of the fact that some gods have an inability to answer certain questions. Neither True nor False can provide an answer to the following question.