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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the number of solutions of Diophantine equations
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by Martin Davis PDF
Proc. Amer. Math. Soc. 35 (1972), 552-554 Request permission

Abstract:

For any nontrivial set of cardinal numbers $\leqq {\aleph _0}$, 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.
References
  • Martin Davis, An explicit diophantine definition of the exponential function, Comm. Pure Appl. Math. 24 (1971), 137–145. MR 272751, DOI 10.1002/cpa.3160240205
    • Ju. V. Matijasevič, Enumerable sets are Diophantine, Dokl. Akad. Nauk SSSR 191 (1970), 279-282=Soviet Math. Dokl. 11 (1970), 354-358.
  • Julia Robinson, Hilbert’s tenth problem, 1969 Number Theory Institute (Proc. Sympos. Pure Math., Vol. XX, State Univ. New York, Stony Brook, N.Y., 1969) Amer. Math. Soc., Providence, R.I., 1971, pp. 191–194. MR 0316234
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 35 (1972), 552-554
  • MSC: Primary 10N05; Secondary 02E10
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0304347-1
  • MathSciNet review: 0304347