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Volumn 91, Issue 4, 1999, Pages 367-378

A binomial representation of the 3x + 1 problem

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EID: 0033475423     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa-91-4-367-378     Document Type: Article
Times cited : (6)

References (20)
  • 1
    • 0001540194 scopus 로고
    • Hilbert's tenth problem. Diophantine equations: Positive aspects of a negative solution
    • Amer. Math. Soc.
    • M. Davis, Yu. Matijasevich and J. Robinson, Hubert's tenth problem. Diophantine equations: positive aspects of a negative solution, in: Proc. Sympos. Pure Math. 28, Amer. Math. Soc., 1976, 323-378.
    • (1976) Proc. Sympos. Pure Math. , vol.28 , pp. 323-378
    • Davis, M.1    Matijasevich, Yu.2    Robinson, J.3
  • 2
    • 0000963095 scopus 로고
    • The decision problem for exponential Diophantine equations
    • M. Davis, H. Putnam and J. Robinson, The decision problem for exponential Diophantine equations, Ann. of Math. 74 (1961), 425-436.
    • (1961) Ann. of Math. , vol.74 , pp. 425-436
    • Davis, M.1    Putnam, H.2    Robinson, J.3
  • 3
    • 34347193348 scopus 로고
    • Über formal unentscheidbare sätze der principia mathematica und verwandter systeme I
    • K. Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme. I, Monatsh. Math. Phys. 38 (1931), 173-198.
    • (1931) Monatsh. Math. Phys. , vol.38 , pp. 173-198
    • Gödel, K.1
  • 4
    • 0000746428 scopus 로고    scopus 로고
    • On a combinatorial expression concerning Fermat's last theorem
    • 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.
    • (1997) Adv. in Appl. Math. , vol.18 , pp. 216-219
    • Hsu, L.C.1    Shiue, P.J.-S.2
  • 5
    • 84941463148 scopus 로고
    • Über die ergänzungssätze zu den allgemeinen reciprocitätsgesetzen
    • E. E. Kummer, Über die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen, J. Reine Angew. Math. 44 (1852), 93-146.
    • (1852) J. Reine Angew. Math. , vol.44 , pp. 93-146
    • Kummer, E.E.1
  • 6
    • 0002747273 scopus 로고
    • The 3x + 1 problem and its generalizations
    • 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).
    • (1985) Amer. Math. Monthly , vol.92 , pp. 3-23
    • Lagarias, J.C.1
  • 7
    • 0009324478 scopus 로고
    • The 3x + 1 problem and its generalizations
    • Burnaby, Amer. Math. Soc., Providence, RI, 1995
    • -, The 3x + 1 problem and its generalizations, in: J. Borwein et al. (eds.), Organic Mathematics (Burnaby, 1995), Amer. Math. Soc., Providence, RI, 1995.
    • (1995) Organic Mathematics
    • Borwein, J.1
  • 9
    • 0001106403 scopus 로고
    • A necessary and sufficient condition for primality, and its source
    • 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.
    • (1972) J. Combin. Theory Ser. A , vol.13 , pp. 131-134
    • Mann, H.B.1    Shanks, D.2
  • 10
    • 0009318203 scopus 로고    scopus 로고
    • Frontier between decidability and undecidability: A survey
    • to appear
    • M. Margenstern, Frontier between decidability and undecidability: a survey, Theoret. Comput. Sci. (1999), to appear.
    • (1999) Theoret. Comput. Sci.
    • Margenstern, M.1
  • 11
    • 0001724572 scopus 로고
    • A class of primality criteria formulated in terms of the divisibility of binomial coefficients
    • in Russian
    • 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.
    • (1977) Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) , vol.67 , pp. 167-183
    • Matiyasevich, Ju.V.1
  • 12
    • 0000725340 scopus 로고
    • 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.
    • (1981) J. Soviet Math. , vol.16 , pp. 874-885
  • 13
    • 0009323259 scopus 로고    scopus 로고
    • Some arithmetical restatements of the four color conjecture
    • to appear; mirrored at http://www.informatik.uni-stuttgart.de/ifi/ti/personen/ Matiyasevich/Journal/4cc
    • -, 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.
    • Theoret. Comput. Sci.
  • 14
    • 0004269968 scopus 로고
    • Moscow, Fizmatlit, in Russian. English transl.: MIT Press, 1993. French transl.: Masson, 1995 mirrored at http://www.informatik.uni-stuttgart.de/ifi/ti/ personen/Matiyasevich/H10Pbook
    • -, 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.
    • (1993) Hilbert's Tenth Problem
  • 15
    • 2142746675 scopus 로고
    • Busy beaver competition and Collatz-like problems
    • P. Michel, Busy beaver competition and Collatz-like problems, Arch Math Logic 32 (1993), 351-367.
    • (1993) Arch Math Logic , vol.32 , pp. 351-367
    • Michel, P.1
  • 16
  • 17
    • 0011668788 scopus 로고
    • Notes on binomial coefficients. I, II, III
    • D. Singmaster, Notes on binomial coefficients. I, II, III, J. London Math Soc. (2) 8 (1974), 545-548, 549-554, 555-560.
    • (1974) J. London Math Soc. , vol.8 , Issue.2 , pp. 545-548
    • Singmaster, D.1
  • 18
    • 0000189235 scopus 로고    scopus 로고
    • An update on the four-colour theorem
    • http://www.ams.org/notices/199807/thomas.pdf
    • 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).
    • (1998) Notices Amer. Math. Soc. , vol.45 , pp. 848-859
    • Thomas, R.1
  • 19
    • 0001169022 scopus 로고
    • An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral identities
    • H. S. Wilf and D. Zeilberger, An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral identities, Invent. Math. 108 (1992), 575-633
    • (1992) Invent. Math. , vol.108 , pp. 575-633
    • Wilf, H.S.1    Zeilberger, D.2
  • 20
    • 0003339117 scopus 로고    scopus 로고
    • The dynamical system generated by the 3n+l function
    • Springer, Berlin
    • G. J. Wirsching, The Dynamical System Generated by the 3n+l Function, Lecture Notes in Math. 1681, Springer, Berlin, 1998.
    • (1998) Lecture Notes in Math. , vol.1681
    • Wirsching, G.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.