Some decidable Diophantine problems: positive solution to a problem of Davis, Matijasevič and Robinson
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- by Moshe Koppel PDF
- Proc. Amer. Math. Soc. 77 (1979), 319-323 Request permission
Abstract:
An algorithm is given for determining whether or not a finite system of conditions of the types $a|B,a < B$, a is a square, possess a simultaneous solution in positive integers. Various generalizations are also obtained.References
- 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., Northern Illinois Univ., De Kalb, Ill., 1974) Amer. Math. Soc., Providence, R.I., 1976, pp. 323–378. (loose erratum). MR 0432534 —, Unsolvable problems, Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977, pp. 567-594.
- 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
- Julia Robinson, Definability and decision problems in arithmetic, J. Symbolic Logic 14 (1949), 98–114. MR 31446, DOI 10.2307/2266510 Edward Schwartz, Existential definability in terms of some quadratic functions, Doctoral Dissertation, Yeshiva University, 1974. Th. Skolem, Diophantische Gleichungen, Ergebnisse der Math. und ihrer Grenzgebiete, Band 5, Springer, Berlin, 1938.
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 77 (1979), 319-323
- MSC: Primary 10N05; Secondary 03B25, 10B99
- DOI: https://doi.org/10.1090/S0002-9939-1979-0545589-6
- MathSciNet review: 545589