ArticleOriginal scientific text

Title

Optimal bounds for the length of rational Collatz cycles

Authors 1, 2

Affiliations

  1. Mathematik Departement, ETH Zürich, CH-8092 Zürich, Switzerland
  2. IMA, University of Minnesota, 514 Vincent Hall, 206 Church Street S.E., Minneapolis, Minnesota 55455, U.S.A.

Bibliography

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  2. J. M. Dolan, A. F. Gilman and S. Manickam, A generalization of Everett's result on the Collatz 3x+1 problem, Adv. in Appl. Math. 8 (1987), 405-409.
  3. S. Eliahou, The 3x+1 problem: New lower bounds on nontrivial cycle lengths, Discrete Math. 118 (1993), 45-56.
  4. I. Krasikov, How many numbers satisfy the 3x+1 conjecture ? Internat. J. Math. Sci. 12(4) (1989), 791-796.
  5. J. C. Lagarias, The 3x+1-problem and its generalizations, Amer. Math. Monthly 92 (1985), 3-23.
  6. J. C. Lagarias, The set of rational cycles for the 3x+1 problem, Acta Arith. 56 (1990), 33-53.
  7. G. Leavens and M. Vermeulen, private communication.
  8. J. W. Sander, On the (3N+1)-conjecture, Acta Arith. 55 (1990), 241-248.
  9. B. G. Seifert, On the arithmetic of cycles for the Collatz-Hasse(Syracuse) conjectures, Discrete Math. 68 (1988), 293-298.
  10. G. Wirsching, An improved estimate concerning 3n+1 predecessor sets, Acta Arith. 63 (1993), 205-210.
Pages:
227-239
Main language of publication
English
Received
1995-09-14
Accepted
1995-11-16
Published
1997
Exact and natural sciences