On the number of solutions of Diophantine equations-Reference-Cited by-同舟云学术

On the number of solutions of Diophantine equations

Published:1972 Issue:2 Volume:35 Page:552-554
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Davis Martin

Abstract

For any nontrivial set of cardinal numbers ≦ ℵ 0 \leqq {\aleph _0} , it is shown that there is no algorithm for testing whether or not the number of positive integer solutions of a given polynomial Diophantine equation belongs to the set.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1972-035-02/S0002-9939-1972-0304347-1/S0002-9939-1972-0304347-1.pdf

Reference3 articles.

1. An explicit diophantine definition of the exponential function;Davis, Martin;Comm. Pure Appl. Math.,1971

2. Ju. V. Matijasevič, Enumerable sets are Diophantine, Dokl. Akad. Nauk SSSR 191 (1970), 279-282=Soviet Math. Dokl. 11 (1970), 354-358.

3. Hilbert’s tenth problem;Robinson, Julia,1971

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