Diophantine problem
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Diophantine set — In mathematics, a Diophantine equation is an equation of the form P(x1, ..., xj, y1, ..., yk)=0 (usually abbreviated P(x,y)=0 ) where P(x,y) is a polynomial with integer coefficients. A Diophantine set is a subset S of Nj [1] so that for some… … Wikipedia
Diophantine equation — In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for… … Wikipedia
Diophantine approximation — In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers. The absolute value of the difference between the real number to be approximated and… … Wikipedia
Coin problem — With only 2 pence and 5 pence coins, one cannot make 3 pence, but one can make any higher amount. The coin problem (also referred to as the Frobenius coin problem or Frobenius problem, after the mathematician Ferdinand Frobenius) is a… … Wikipedia
Hilbert's tenth problem — is the tenth on the list of Hilbert s problems of 1900. Its statement is as follows:Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it… … Wikipedia
Glossary of arithmetic and Diophantine geometry — This is a glossary of arithmetic and Diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of… … Wikipedia
Undecidable problem — In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is impossible to construct an algorithm that leads to a yes or no answer the problem is not decidable.A decision problem is any … Wikipedia
Brocard's problem — asks to find integer values of n for which :n!+1 = m^2, where n! is the factorial. It was posed by H. Brocard in a pair of articles in 1876 and 1885, and independently in 1913 by Ramanujan.Brown numbersPairs of the numbers ( n , m ) that solve… … Wikipedia
Znám's problem — In number theory, Znám s problem asks which sets of k integers have the property that each integer in the set is a proper divisor of the product of the other integers in the set, plus 1. Znám s problem is named after the Slovak mathematician… … Wikipedia
Lattice problem — In computer science, lattice problems are a class of optimization problems on lattices. The conjectured intractability of such problems is central to construction of secure lattice based cryptosystems. For applications in such cryptosystems,… … Wikipedia
Archimedes' 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… … Wikipedia
