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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, Mathematical developments arising from Hilbert problems (Proc. Sympos. Pure Math., Vol. XXVIII, Northern Illinois Univ., De Kalb, Ill., 1974) Amer. Math. Soc., Providence, R. I., 1976, pp. 323–378. (loose erratum). MR 0432534
  • [2] -, Unsolvable problems, Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977, pp. 567-594.
  • [3] N. K. Kosovskiĭ, The solution of systems that consist simultaneously of word equations and word length inequalities, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 40 (1974), 24–29, 156 (Russian, with English summary). Investigations in constructive mathematics and mathematical logic, VI (dedicated to A. A. Markov on the occasion of his 70th birthday). MR 0373863
  • [4] Julia Robinson, Definability and decision problems in arithmetic, J. Symbolic Logic 14 (1949), 98–114. MR 0031446,
  • [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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