Universal diophantine equation

Keywords

Diophantine equation, Recursively enumerable language, Recursively enumerable set, Diophantine set, Maximal set

References

• Diophantine representation of Mersenne and Fermat primesJames C. Peyton Jones — 1979
• Reduction of an arbitrary diophantine equation to one in 13 unknownsYuri Matijasevič, Julia Robinson — 1975
• A new proof of the theorem on exponential diophantine representation of enumerable setsYuri Matiyasevich — 1980
• Notes on Binomial Coefficients Iii—Any Integer Divides Almost All Binomial Coefficients†David Singmaster — 1974
• Existential definability in arithmeticJulia Robinson — 1952
• Three universal representations of recursively enumerable setsJames P. Jones — 1978
• DIOPHANTINE REPRESENTATION OF THE SET OF PRIME NUMBERSJames P. Jones, Daihachiro Sato, Hideo Wada — 1976
• Hilbert's Tenth Problem is UnsolvableMartin Davis — 1973
• Undecidable diophantine equationsJames P. Jones — 1980
• A class of primality criteria formulated in terms of the divisibility of binomial coefficientsYuri Matiyasevich — 1981
• Arithmetical representations of enumerable sets with a small number of quantifiersYuri Matiyasevich — 1976
• Primes are nonnegative values of a polynomial in 10 variablesYu. V. Matijasevič — 1981
• The Decision Problem for Exponential Diophantine EquationsHartley Rogers — 1961
• On Recursive Unsolvability of Hilbert's Tenth ProblemYu. V. Matijasevič — 1973
• Some Purely Mathematical Results Inspired by Mathematical LogicYu. V. Matijasevič — 1977
• Zur Theorie der quadratischen FormenC. Siegel — 1972

Cited by

• Theoretical Foundations for Practical 'Totally Functional Programming'Colin Kemp — 2007
• Appendix: Details on Experiments (Counting and Estimating Lattice Points)Jesús A. De Loera — 2009
• Seeking a proof to a mathematical proposition and Diophantine equationTao Mei — 2005
• Unification and equation solving in nilpotent groups and monoidsEdmund Burke — 1991
• Undecidable proposition in PA and Diophantine equationTao Mei — 2005
• On weak number theoriesTung SHIH-PING — 1985
• Definability, decidability, complexityPatrick Cégielski — 1996
• Diophantine cryptography in free metabelian groups: Theoretical baseAlexei Myasnikov, В. А. Романьков — 2014
• How to pick out the integers in the rationals: an application of number theory to logicDan Flath, Stan Wagon — 1991
• Mathematical programming: Turing completeness and applications to software analysisLeo Liberti, Fabrizio Marinelli — 2014
• On a Diophantine Representation of the Predicate of ProvabilityM. Carl, B. Z. Moroz — 2014
• THE SOLVABILITY PROBLEM FOR EQUATIONS IN ONE UNKNOWN IN NILPOTENT GROUPSNadya Repin — 1985
• Undecidability and incompleteness in classical mechanicsNewton C. A. da Costa, Francisco Antônio Dória — 1991
• On the decidability of phase ordering problem in optimizing compilationSid‐Ahmed‐Ali Touati, Denis Barthou — 2006
• On the computability of Nash equilibriaKislaya Prasad — 1997
• Computational Complexities of Diophantine Equations with ParametersShih‐Ping Tung — 1987
• The Scope of Gödel’s First Incompleteness TheoremBernd Buldt — 2014
• Classical physics and Penrose's thesisNewton C. A. da Costa, Francisco Antônio Dória — 1991
• Infinite sets of primes, admitting diophantine representations in eight variablesMaxim Vsemirnov — 1997
• Elimination of quantifiers from arithmetical formulas defining recursively enumerable setsYuri Matiyasevich — 2004

Related papers

• A New Proof of Smoryński’s TheoremApoloniusz Tyszka — 2017
• A New Proof of Smoryński’s TheoremApoloniusz Tyszka — 2017
• A Direct Method for Simulating Partial Recursive Functions by Diophantine EquationsYuri Matiyasevich — 1994
• Diophantine representations of recursive enumerable setsNiels Voorneveld — 2013
• Reductions of Hilbert's tenth problemMartin Davis, Hilary Putnam — 1958
• Diophantine Equations with a Finite Number of Solutions: Craig Smorynski's Theorem, Harvey Friedman's Conjecture and Minhyong Kim's GuessApoloniusz Tyszka — 2019