ONE EQUATION TO RULE THEM ALL

Abstract

The report describes an application of recursive function theory to Hilbert's tenth problem. It is proved that if a particular exhibited diophantine equation has no nontrivial solutions, then all recursively enumerable sets are diophantine. Hence, if the exhibited diophantine equation has no nontrivial solutions, then Hilbert's tenth problem is recursively unsolvable. The methods used can be readily adapted to obtained various other hypotheses about which demonstrations can be made similar to the one given in this study. It has not yet been proved that the 'one equation to rule them all' has no nontrivial solution, but so far the search for counterexamples has been fruitless.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1968
Accession Number
AD0665414

Entities

People

  • Martin Davis

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Computations
  • Computer Programs
  • Difference Equations
  • Equations
  • Mathematical Logic
  • Mathematics
  • New York
  • Number Theory
  • Numbers
  • Polynomials
  • Prime Numbers
  • Recursive Functions
  • Theorems
  • United States

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.
  • Systems Analysis and Design