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Hilbert's tenth problem

Known as: Hilbert's 10th problem, Hilberts tenth problem, 10th Hilbert problem 
Hilbert's tenth problem is the tenth on the list of Hilbert's problems of 1900. Its statement is as follows: Given a Diophantine equation with any… Expand
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Papers overview

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2019
2019
We formalise the undecidability of solvability of Diophantine equations, i.e. polynomial equations over natural numbers, in Coq's… Expand
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2017
2017
For a ring R, Hilbert’s Tenth Problem HTP(R) is the set of polynomial equations over R, in several variables, with solutions in R… Expand
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Highly Cited
2009
Highly Cited
2009
Abstract This study employed life cycle assessment (LCA) to quantify and compare the potential environmental impacts of culturing… Expand
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2008
2008
We show a reduction of Hilbert's tenth problem to the solvability of the matrix equation over non-commuting integral matrices… Expand
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Highly Cited
2006
Highly Cited
2006
1. Introduction 2. Diophantine classes: definition and basic facts 3. Diophantine equivalence and diophantine decidability 4… Expand
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Highly Cited
2001
Highly Cited
2001
We explore in the framework of Quantum Computation the notion of Computability, which holds a central position in Mathematics and… Expand
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Highly Cited
2000
Highly Cited
2000
This essay discusses the effect of technical change on wage inequality. I argue that the behavior of wages and returns to… Expand
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Highly Cited
1993
Highly Cited
1993
At the 1900 International Congress of Mathematicians, held that year in Paris, the German mathematician David Hilbert put forth a… Expand
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Highly Cited
1973
Highly Cited
1973
When a long outstanding problem is finally solved, every mathematician would like to share in the pleasure of discovery by… Expand
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1958
1958
(1) (Eyl)... (Eym)[P(yi, Y2, ** Ymin X1, X2, xn) = 01 where P is a polynomial with integral coefficients (positive, negative, or… Expand
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