Tham khảo Giả thuyết Collatz

  1. ↑ O'Connor, J.J.; Robertson, E.F. (2006). “Lothar Collatz”. St Andrews University School of Mathematics and Statistics, Scotland.
  2. ↑ Maddux, Cleborne D.; Johnson, D. Lamont (1997). Logo: A Retrospective. New York: Haworth Press. tr. 160. ISBN 0-7890-0374-0. The problem is also known by several other names, including: Ulam's conjecture, the Hailstone problem, the Syracuse problem, Kakutani's problem, Hasse's algorithm, and the Collatz problem.
  3. 1 2 Lagarias, Jeffrey C. (1985). “The 3x + 1 problem and its generalizations”. The American Mathematical Monthly. 92 (1): 3–23. JSTOR 2322189.
  4. ↑ According to Lagarias (1985)[3] p. 4, the name "Syracuse problem" was proposed by Hasse in the 1950s, during a visit to Syracuse University.
  5. ↑ Pickover, Clifford A. (2001). Wonders of Numbers. Oxford: Oxford University Press. tr. 116–118. ISBN 0-19-513342-0.
  6. ↑ “Hailstone Number”. MathWorld. Wolfram Research.
  7. ↑ Hofstadter, Douglas R. (1979). Gödel, Escher, Bach. New York: Basic Books. tr. 400–2. ISBN 0-465-02685-0.
  8. ↑ Guy, Richard K. (2004). “"E17: Permutation Sequences"”. Unsolved problems in number theory (ấn bản 3). Springer-Verlag. tr. 336–7. ISBN 0-387-20860-7. Zbl 1058.11001.
  9. ↑ Guy, R. K. (1983). “Don't try to solve these problems”. Amer. Math. Monthly. 90: 35–41. doi:10.2307/2975688. JSTOR 2975688. By this Erdos means that there aren't powerful tools for manipulating such objects.
  10. ↑ Lagarias, Jeffrey C. biên tập (2010). The ultimate challenge: the 3x+1 problem. Providence, R.I.: American Mathematical Society. tr. 4. ISBN 0821849409.
  11. ↑ Leavens, Gary T.; Vermeulen, Mike (tháng 12 năm 1992). “3x+1 Search Programs”. Computers & Mathematics with Applications. 24 (11): 79–99. doi:10.1016/0898-1221(92)90034-F.
  12. ↑ Roosendaal, Eric. “3x+1 Delay Records”. Truy cập ngày 30 tháng 6 năm 2017. (Note: "Delay records" are total stopping time records.)
  13. ↑ Lagarias, Jeffrey C. biên tập (2010). The Ultimate Challenge: the 3x+1 problem. American Mathematical Society. ISBN 978-0-8218-4940-8. Zbl 1253.11003.

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