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Литература
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| 1. |
A. Baker, H. Davenport,, “The equations $3x^2-2=y^2$ and $8x^2-7=z^2$”, Quart. J. Math. Oxford Ser. (2), 20 (1969), 129–137    |
| 2. |
G. Chaitin, Algorithmic Information Theory, Cambridge University Press, Cambridge, England, 1987 |
| 3. |
Г. В. Чудновский, Некоторые алгоритмические проблемы, Препринт IM-71-3, АН Укр. ССР, Институт Математики, Киев, 1971 |
| 4. |
G. V. Chudnovsky, “Some Diophantine problems”, Contributions to the theory of transcendental numbers, Math. Surveys Monogr., 19, Amer. Math. Soc., Providence, RI, 1984, 265–295 |
| 5. |
M. Davis, “Arithmetical problems and recursively enumerable predicates”, J. Symbolic Logic, 18:1 (1953), 33–41 |
| 6. |
M. Davis, H. Putnam, J. Robinson, “The decision problem for exponential Diophantine equations”, Ann. Math. (2), 74 (1961), 425–436 ; reprinted in: S. Feferman (ed.), The collected works of Julia Robinson, Collected Works, v. 6, Amer. Math. Soc., Providence, RI, 1996 |
| 7. |
M. Davis, “One equation to rule them all”, Transactions of the New York Academy of Sciences. Series II, 30:6 (1968), 766–773 |
| 8. |
M. Davis, “On the number of solutions of Diophantine equations”, Proc. Amer. Math. Soc., 35 (1972), 552–554 |
| 9. |
O. Herrman, “A nontrivial solution of the Diophantine equation $9(x^2+7y^2)^2-7(u^2+7v^2)^2=2$”, Computers in Number Theory, eds. A. O. L. Atkin, B. J. Birch, Academic Press, London, 1971, 207–212 |
| 10. |
D. Hilbert, “Mathematische Probleme”, Vortrag, gehalten auf dem internationalen Mathematiker Kongress zu Paris 1900, Nachr. K. Ges. Wiss., Math. Phys. Kl., Göttingen, 1900, 253–297 ; English translation: Reprinted in: Mathematical Developments arising from Hilbert problems, Proceedings of Symposia in Pure Mathematics, 28, ed. Browder Ed., American Mathematical Society, 1976, 1–34  |
| 11. |
J. P. Jones, Yu. V. Matijasevič, “A new representation for the symmetric binomial coefficient and its applications”, Annales Sci. Mathém. du Québec, 6:1 (1982), 81–97 |
| 12. |
E. E. Kummer, “Über die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen”, J. reine angew. Math., 44 (1852), 93–146 |
| 13. |
D. H. Lehmer, “Continued fractions containing arithmetic progressions”, Scripta Math., 29 (1973), 17–24 |
| 14. |
H. Levitz, “Decidability of some problem pertaining to base 2 exponential Diophantine equations”, Zeitschrift Math. Logik Grundlagen Math., 31:2 (1985), 109–115  |
| 15. |
Ю. В. Матиясевич, “Диофантовость перечислимых множеств”, ДАН СССР, 191:2 (1970), 279–282  ; English translation: “Enumerable sets are Diophantine”, Soviet Math. Dokl., 11 (1970), 354–358 |
| 16. |
Ю. В. Матиясевич, “Существование неэффективизируемых оценок в теории экспоненциально диофантовых уравнений”, Зап. научн. семин. ЛОМИ, 40, 1974, 77–93 ; English translation: “Existence of noneffectivizable estimates in the theory of exponential Diophantine equations”, J. of Soviet Mathematics, 8:3 (1977), 299–311 |
| 17. |
Ю. В. Матиясевич, “Алгоритмическая неразрешимость экспоненциально диофантовых уравнений с тремя неизвестными”, Теория алгорифмов и математическая логика, ВЦ АН СССР, Москва, 1979, 69–78 ; English translation: “Algorithmic unsolvability of exponential Diophantine equations in three unknowns”, Sel. Math. Sov., 3 (1984), 223–232 |
| 18. |
Ю. В. Матиясевич, Десятая проблема Гильберта, Наука, Физматлит, Москва, 1993 ; English translation: Hilbert's Tenth Problem, MIT Press, Cambridge (Massachusetts)–London, 1993 ; French translation: Le dixième Problème de Hilbert, Masson, Paris–Milan–Barselone, 1995; http://logic.pdmi.ras.ru/~yumat/H10Pbook |
| 19. |
Yu. Matiyasevich, “Diophantine flavor of Kolmogorov complexity”, Trans. Inst. Informatics and Automation Problems National Acad. Sciences of Armenia, 27 (2006), 111–122 |
| 20. |
J. Mc Laughlin, “Some new families of Tasoevian and Hurwitzian continued fractions”, Acta Arith., 135:3 (2008), 247–268 |
| 21. |
T. Ord, T. D. Kieu, “On the existence of a new family of Diophantine equations for $\Omega$”, Fundam. Inform., 56:3 (2003), 273–284 |
| 22. |
K. Prasad, “Computability and randomness of Nash equilibrium in infinite games”, J. Mathem. Economics, 20:5 (1991), 429–442 |
| 23. |
P. Riyapan, V. Laohakosol, T. Chaichana, “Two types of explicit continued fractions”, Period. Math. Hungar., 52:2 (2006), 51–72 |
| 24. |
J. Robinson, “Existential definability in arithmetic”, Transactions of the American Mathematical Society, 72 (1952), 437–449 ; reprinted in: The Collected Works of Julia Robinson, Collected Works, 6, American Mathematical Society, Providence, RI, 1996, 47–59 |
| 25. |
D. Shanks, S. S. Wagstaff Jr., “48 more solutions of Martin Davis's quaternary quartic equation”, Math. Comp., 64:212 (1995), 1717–1731 |
| 26. |
C. Smoryński, “A note on the number of zeros of polynomials and exponential polynomials”, J. Symbolic Logic, 42:1 (1977), 99–106 |
| 27. |
Б. Г. Тасоев, “Рациональные проиближения к некоторым бесконечным цепным дробям”, Труды тбилисского университета. Мат., мех., астроном., 24, 1988, 104–138 |
