# 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  gives an algorithm for all polynomials P(xx, . . . , xv) of degree < 2. From the work of A. Baker  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
Matijasevic's theorem implies the existence of a diophantine equation U such that for all x and v, x ∈ W v is also recursively enumerable, and the nonexistence of such an algorithm follows immediately from theexistence of r.e. nonrecursive sets.
1 Hilbert ’ s Tenth Problem
Hilbert’s 10th problem, stated in modern terms, is Find an algorithm that will, given p ∈ Z[x1, . . . , xn], determine if there exists a1, . . . , an ∈ Z such that p(a1, . . . , an) = 0. Davis,
Extensions of Hilbert's tenth problem
• 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.
The Fixed Point Problem for General and for Linear SRL Programs is Undecidable
• Computer Science
ICTCS
• 2018
It is shown that the existence of xed points in SRL is undecidable and complete in Σ 1 and that the problem of deciding if there is a tuple of initial register values of a given program P that remains unaltered after the execution of P.
A universal differential equation
REMARK 1. From the proof, it will be clear that we can in addition ensure that y(tj) — y(tj) for any sequence (tj) of distinct real numbers such that \tj\ —* °° as ƒ —> oo. REMARK 2. We may moreover
POINTS AND SUBSPACES OF SMALL HEIGHT IN QUADRATIC AND LINEAR SPACES
• Mathematics
• 2012
We investigate a few related questions on search bounds via height for rational points over global fields in quadratic and linear spaces. Specifically, let K be a global field or Q and N ≥ 2 an
Finding Zeros of Rational Quadratic Forms
In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. We begin by discussing Diophantine equations, the field of p-adic numbers, and the Hasse-Minkowski
Representing integers by multilinear polynomials
• Mathematics
• 2020
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