Geodesic
What can and cannot be done with Diophantine problems
Informatics and Automation, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 128-143

Voir la notice de l'article provenant de la source Math-Net.Ru

This survey presents various theorems (obtained mainly by specialists in mathematical logic and computability theory) stating the impossibility of algorithms for solving certain Diophantine problems. Often the technique developed for obtaining such “negative” results also allows one to prove many “positive” theorems on the possibility of formulating Diophantine problems with special properties. This survey also lists a number of questions that remain open. 
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     author = {Yu. V. Matiyasevich},
     title = {What can and cannot be done with {Diophantine} problems},
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     year = {2011},
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     url = {http://geodesic.mathdoc.fr/item/TRSPY_2011_275_a6/}
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Yu. V. Matiyasevich. What can and cannot be done with Diophantine problems. Informatics and Automation, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 128-143. http://geodesic.mathdoc.fr/item/TRSPY_2011_275_a6/