# Collatz cycles with few descents

Acta Arithmetica (2000)

- Volume: 92, Issue: 2, page 181-188
- ISSN: 0065-1036

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top## How to cite

topT. Brox. "Collatz cycles with few descents." Acta Arithmetica 92.2 (2000): 181-188. <http://eudml.org/doc/207379>.

@article{T2000,

author = {T. Brox},

journal = {Acta Arithmetica},

keywords = { problem; Collatz problem; Collatz cycles; descending integer; linear forms in logarithms},

language = {eng},

number = {2},

pages = {181-188},

title = {Collatz cycles with few descents},

url = {http://eudml.org/doc/207379},

volume = {92},

year = {2000},

}

TY - JOUR

AU - T. Brox

TI - Collatz cycles with few descents

JO - Acta Arithmetica

PY - 2000

VL - 92

IS - 2

SP - 181

EP - 188

LA - eng

KW - problem; Collatz problem; Collatz cycles; descending integer; linear forms in logarithms

UR - http://eudml.org/doc/207379

ER -

## References

top- [1] A. Baker, Transcendental Number Theory, Cambridge Univ. Press, 1975. Zbl0297.10013
- [2] E. G. Belaga and M. Mignotte, Embedding the 3x + 1 conjecture in a 3x + d context, Experiment. Math. 7 (1998), 145-152. Zbl0918.11008
- [3] L. Halbeisen and N. Hungerbühler, Optimal bounds for the length of rational Collatz cycles, Acta Arith. 78 (1997), 227-239. Zbl0863.11015
- [4] J. C. Lagarias, The 3x + 1 problem and its generalizations, Amer. Math. Monthly 92 (1985), 3-23. Zbl0566.10007
- [5] J. C. Lagarias, The set of rational cycles for the 3x + 1 problem, Acta Arith. 56 (1990), 33-53. Zbl0773.11017
- [6] R. P. Steiner, A theorem on the Syracuse Problem, in: Proc. 7th Manitoba Conf. on Numerical Mathematics, 1977, Winnipeg, 1978, 553-559.
- [7] G. J. Wirsching, The Dynamical System Generated by the 3n + 1 Function, Lecture Notes in Math. 1681, Springer, Berlin, 1998. Zbl0892.11002

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