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A binomial representation of the 3x + 1 problem

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Twórcy
  • Université de Metz, I.U.T. de Metz, Groupe d'Informatique Fondamentale de Metz, Île du Saulcy, 57045 Metz Cedex, France
  • Steklov Institute of Mathematics at Sankt-Petersburg, Laboratory of Mathematical Logic, Fontanka 27, 191011 Sankt-Petersburg, Russia
Bibliografia
  • [1] M. Davis, Yu. Matijasevich and J. Robinson, Hilbert's tenth problem. Diophantine equations: positive aspects of a negative solution, in: Proc. Sympos. Pure Math. 28, Amer. Math. Soc., 1976, 323-378.
  • [2] M. Davis, H. Putnam and J. Robinson, The decision problem for exponential Diophantine equations, Ann. of Math. 74 (1961), 425-436.
  • [3] K. Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme. I, Monatsh. Math. Phys. 38 (1931), 173-198.
  • [4] L. C. Hsu and P. J.-S. Shiue, On a combinatorial expression concerning Fermat's Last Theorem, Adv. in Appl. Math. 18 (1997), 216-219.
  • [5] E. E. Kummer, Über die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen, J. Reine Angew. Math. 44 (1852), 93-146.
  • [6] J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly 92 (1985), 3-23 (available at: http://www.cecm.sfu.ca/organics/papers/lagarias/index.html).
  • [7] J. C. Lagarias, The 3x+1 problem and its generalizations, in: J. Borwein et al. (eds.), Organic Mathematics (Burnaby, 1995), Amer. Math. Soc., Providence, RI, 1995.
  • [8] J. C. Lagarias, 3x+1 Problem Annotated Bibliography, http://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/local/anno_bib.ps.
  • [9] H. B. Mann and D. Shanks, A necessary and sufficient condition for primality, and its source, J. Combin. Theory Ser. A 13 (1972), 131-134.
  • [10] M. Margenstern, Frontier between decidability and undecidability: a survey, Theoret. Comput. Sci. (1999), to appear.
  • [11] Ju. V. Matijasevič [Yu. V. Matiyasevich], A class of primality criteria formulated in terms of the divisibility of binomial coefficients, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 67 (1977), 167-183, 226-227 (in Russian); English transl.: J. Soviet Math. 16 (1981), 874-885.
  • [12] Ju. V. Matijasevič [Yu. V. Matiyasevich], Some arithmetical restatements of the Four Color Conjecture, Theoret. Comput. Sci., to appear; a version is available at: http://logic.pdmi.ras.ru/~yumat/Journal/4cc, mirrored at http://www.informatik.uni-stuttgart.de/ifi/ti/personen/Matiyasevich/Journal/4cc.
  • [13] Ju. V. Matijasevič [Yu. V. Matiyasevich], Hilbert's Tenth Problem, Moscow, Fizmatlit, 1993 (in Russian). English transl.: MIT Press, 1993. French transl.: Masson, 1995. See also at: http://logic.pdmi.ras.ru/~yumat/H10Pbook, mirrored at http://www.informatik.uni-stuttgart.de/ifi/ti/personen/Matiyasevich/H10Pbook.
  • [14] P. Michel, Busy beaver competition and Collatz-like problems, Arch. Math. Logic 32 (1993), 351-367.
  • [15] M. Petkovšek, H. S. Wilf and D. Zeilberger, A=B, AK Peters, Wellesley, MA, 1996; http://www.cis.upenn.edu/~wilf/AeqB.html.
  • [16] D. Singmaster, Notes on binomial coefficients. I, II, III, J. London Math. Soc. (2) 8 (1974), 545-548, 549-554, 555-560.
  • [17] R. Thomas, An update on the Four-Colour Theorem, Notices Amer. Math. Soc. 45 (1998), 848-859 (available at: http://www.ams.org/notices/199807/thomas.ps, http://www.ams.org/notices/199807/thomas.pdf).
  • [18] H. S. Wilf and D. Zeilberger, An algorithmic proof theory for hypergeometric (ordinary and 'q') multisum/integral identities, Invent. Math. 108 (1992), 575-633.
  • [19] G. J. Wirsching, The Dynamical System Generated by the 3n+1 Function, Lecture Notes in Math. 1681, Springer, Berlin, 1998.
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Bibliografia
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bwmeta1.element.bwnjournal-article-aav91i4p367bwm
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