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Some decidable Diophantine problems: positive solution to a problem of Davis, Matijasevič and Robinson

Author: Moshe Koppel
Journal: Proc. Amer. Math. Soc. 77 (1979), 319-323
MSC: Primary 10N05; Secondary 03B25, 10B99
MathSciNet review: 545589
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Abstract: An algorithm is given for determining whether or not a finite system of conditions of the types $ a\vert B,a < B$, a is a square, possess a simultaneous solution in positive integers. Various generalizations are also obtained.

References [Enhancements On Off] (What's this?)

  • [1] Martin Davis, Yuri Matijasevič and Julia Robinson, Hilbert's tenth problem. Diophantine equations: Positive aspects of a negative solution, Proc. Sympos. Pure Math., vol. 28, Amer. Math. Soc., Providence, R. I., 1976, pp. 323-378. MR 0432534 (55:5522)
  • [2] -, Unsolvable problems, Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977, pp. 567-594.
  • [3] N. K. Kosovskii, On solutions of systems consisting of both word equations and word length inequalities, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 40 (1974), 24-29. (Russian) MR 0373863 (51:10063)
  • [4] Julia Robinson, Definability and decision problems in arithmetic, J. Symbolic Logic 14 (1949), 98-114. MR 0031446 (11:151f)
  • [5] Edward Schwartz, Existential definability in terms of some quadratic functions, Doctoral Dissertation, Yeshiva University, 1974.
  • [6] Th. Skolem, Diophantische Gleichungen, Ergebnisse der Math. und ihrer Grenzgebiete, Band 5, Springer, Berlin, 1938.

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Keywords: Diophantine problems, decidability
Article copyright: © Copyright 1979 American Mathematical Society

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