Fetching the paper…
Reading the bibliography…
Hilbert's 10th problem, stated in modern terms, is: Find an algorithm that will, given $p \in \mathbb{Z}[x_1,\ldots,x_n]$ determine if there exists $a_1, a_2, \ldots, a_n \in \mathbb{Z}$ such that $p(a_1,\ldots,a_n)=0$.
Cracking the problem with 33, 2019
Andrew Booker · 1903
Earlier work this paper cites.
The decision problem for exponential diophantine equations
Martin Davis, Hillary Putnam, and Julia Robinson · 1961
Earlier work this paper cites.
On the representation of integers by binary forms
Alan Baker · 1968
Earlier work this paper cites.
Integer points on curves of genus 1
Alan Baker and John Coates · 1970
Earlier work this paper cites.
Enumerable sets are diophantine (Russian)
Yuri Matijasevič · 1970
Earlier work this paper cites.
Computing all s-integral points on elliptic curves
Attila Petho, Horst G Zimer, Josef Gebel, and Emanuel Herrmann · 1970
Earlier work this paper cites.
Arithmetical representations of enumerable sets with a small number of quantifiers
Yuri Matijasevič · 1972
Earlier work this paper cites.
Zur theorie der quadratischen formen
Carl Ludwig Siegel · 1972
Earlier work this paper cites.
Hilbert’s tenth problem is unsolvable
Martin Davis · 1973
Earlier work this paper cites.
Two universal 3-quantifier representations of recursively enumerable sets
Yuri Matijasevič and Julia Robinson · 1974
Earlier work this paper cites.
Reduction of an arbitrary diophantine equation to one in 13 unknowns
Yuri Matijasevič and Julia Robinson · 1975
Earlier work this paper cites.
Succinct certificates for the solvability of binary quadratic diophantine equations
Jeffrey Lagarias · 1979
Earlier work this paper cites.
Undecidable diophantine equations
James Jones · 1980
Cited alongside, same era.
How to solve a quadratic equations in integers
Fritz J. Grunewald and Dan Segal · 1981
Cited alongside, same era.
Universal diophantine equations
James Jones · 1982
Cited alongside, same era.
Disquisitiones Arithmetica (English Translation)
Carl F. Gauss · 1986
Cited alongside, same era.
The density of zeros of forms for which weak approximation fails
Roger Heath-Brown · 1992
Cited alongside, same era.
A new relation-combining theorem and its application
Zhi-Wei Sun · 1992
Cited alongside, same era.
Hilbert’s Tenth Problem
Yuri Matijasevič · 1993
On the integer solutions of quadratic equations
Fritz J. Grunewald and Dan Segal · 2004
Later among the works it cites.
Faster algorithms for Frobenius Numbers
Dale Beihoffer, Jemimah Hendry, Albert Nijenhuis, and Stan Wagon · 2005
Later among the works it cites.
On the solvability of a class of diophantine equations and applications
Oscar Ibarra and Zhe Dang · 2006
Later among the works it cites.
New sums of three cubes
Andreas-Stephan Elsehans and Jorg Jahnel · 2009
Later among the works it cites.
Problems in number theory from busy beaver competitions, 2013
Pascal Michel · 2013
Later among the works it cites.
Newer sums of three cubes, 2016
Sander Huisman · 2016
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Points entiers sur les courbes de genre 0
Dimitrios Poulakis · 1993
Cited alongside, same era.
A polynomial time algorithm for diophantine equations in one variable
Felipe Cucker, Pascal Koiran, and Steve Smale · 1999
Cited alongside, same era.
Rational points near curves and small nonzero | x 3 − y 3 | |x^{3}-y^{3}| via lattice reductions
Noam Elkies · 2000
Cited alongside, same era.
Solving genus zero diophantine equations with at most two infinite valuations
Dimitrios Poulakis · 2002
Cited alongside, same era.
Computing all integer solutions of a genus 1 equation
Roel Stoeker and Nikoluas Tzanakis · 2003
Cited alongside, same era.
Later among the works it cites.
A relatively small Turing machine whose behaviour is independent of set theory, 2016
Adam Yedidia and Scott Aaronson · 2016
Later among the works it cites.
Rational points on varieties
Bjorn Poonen · 2017
Later among the works it cites.
Beeindruckende mathematik-erfolge im, 2018
Jonas Bayer, Marco Davi, Simon Dubischar, Malte Habler, Abnik Pal, and Michael Schmalian und Benedkit Stock Zusammengestellt von Stephanie Schiemann · 2018
Later among the works it cites.
The busy beaver frontier (an open problems column)
Scott Aaronson · 2020
Later among the works it cites.
Further results on Hilbert’s tenth problem
Zhi-Wei Sun · 2020
Later among the works it cites.
Mixed quantifier prefixes over diophantine equations with integer variables, 2021
Zhi-Wei Sun · 2021
Closest in time.