# Undecidable diophantine equations

```@article{Jones1980UndecidableDE,
title={Undecidable diophantine equations},
author={James P. Jones},
journal={Bulletin of the American Mathematical Society},
year={1980},
volume={3},
pages={859-862}
}```
• James P. Jones
• Published 1 September 1980
• Mathematics
• Bulletin of the American Mathematical Society
In 1900 Hubert asked for an algorithm to decide the solvability of all diophantine equations, P(x1, . . . , xv) = 0, where P is a polynomial with integer coefficients. In special cases of Hilbert's tenth problem, such algorithms are known. Siegel [7] gives an algorithm for all polynomials P(xx, . . . , xv) of degree < 2. From the work of A. Baker [1] we know that there is also a decision procedure for the case of homogeneous polynomials in two variables, P(x, y) = c. The first steps toward the…
Universal diophantine equation
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1 Hilbert ’ s Tenth Problem
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• T. Pheidas
• Mathematics
Journal of Symbolic Logic
• 1994
The present article is an attempt to bridge the gap between the researchers that work in the areas adjacent to Hilbert's Tenth Problem (for short, HTP), mainly, number theory and mathematical logic.
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Let \$\$F(\varvec{x})\$\$ be a homogeneous polynomial in \$\$n \ge 1\$\$ variables of degree \$\$1 \le d \le n\$\$ with integer coefficients so that its degree in every variable is equal to 1. We give

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• A. Baker
• Mathematics
Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
• 1968
An effective algorithm is established for solving in integers x, y any Diophantine equation of the type/(x, y) = m, where/ denotes an irreducible binary form with integer coefficients and degree at
Some Purely Mathematical Results Inspired by Mathematical Logic
This chapter discusses results about algorithmical unsolvability of many important decision problems in mathematics that are not purely mathematical since their very formulations involve some logical notions such as the notion of axiomatic theory or that of algorithm.
DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung dieses Dokuments. Dieses Dokument ist ausschließlich für den persönlichen,
Three universal representations of recursively enumerable sets
This article constructs an explicit undecidable arithmetical formula, F(x, n) , in prenex normal form, which is explicit in the sense that it is written out in its entirety with no abbreviations and can be focused into Godel's Incompleteness Theorem.
Baker , Contributions to the theory of diophantine equations . I , Philos
• 1968
Three universal representations of r.e. sets
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Three universal representations of r.e
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