Further results on Hilbert's tenth problem

DOI10.1007/s11425-020-1813-5zbMath1494.11100arXiv1704.03504OpenAlexW3119401540MaRDI QIDQ829448

N. E. Zubov

Publication date: 6 May 2021

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.03504

zbMATH Keywords

undecidabilityintegral solutionDiophantine equationpolygonal numbersHilbert's tenth problem

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Undecidability and degrees of sets of sentences (03D35) Decidability of theories and sets of sentences (03B25) Recursively (computably) enumerable sets and degrees (03D25) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Primes (11A41) Diophantine equations (11D99)

Related Items (3)

Prime representing polynomial ⋮ Existential definability and diophantine stability ⋮ Universally defining Z$\mathbb {Z}$ in Q$\mathbb {Q}$ with 10 quantifiers

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On universal sums of polygonal numbers
• A result similar to Lagrange's theorem
• The decision problem for exponential diophantine equations
• Primes are nonnegative values of a polynomial in 10 variables
• Reduction of unknowns in diophantine representations
• Register machine proof of the theorem on exponential diophantine representation of enumerable sets
• Computational complexities of diophantine equations with parameters
• An unsolvable problem in number theory
• Classification of Quantifier Prefixes Over Diophantine Equations
• Universal diophantine equation
• How to Pick Out the Integers in the Rationals: An Application of Number Theory to Logic
• Hilbert's Tenth Problem for Quadratic Rings
• The Diophantine Problem for Polynomial Rings and Fields of Rational Functions
• Diophantine Sets over Some Rings of Algebraic Integers
• ANEW RELATION‐COMBINING THEOREM AND ITS APPLICATION
• Every Number is Expressible as the Sum of How Many Polygonal Numbers?
• Hilbert's Tenth Problem is Unsolvable
• Reduction of an arbitrary diophantine equation to one in 13 unknowns
• Contributions to the theory of diophantine equations I. On the representation of integers by binary forms
• Definability and decision problems in arithmetic
• Arithmetical Definitions in the Ring of Integers
• Defining \(\mathbb Z\) in \(\mathbb Q\)

This page was built for publication: Further results on Hilbert's tenth problem