I am looking for three papers on the Collatz Conjecture by Charles C. Cadogan. The Annotated Bibliography II (Lagarias) lists these three as:

"Charles C. Cadogan (2000), The 3x+ 1 problem: towards a solution, Caribbean J. Math. Comput. Sci. 10 (2000), paper 2, 11pp. (MR 2005g:11032)"

"Charles C. Cadogan (2003), Trajectories in the 3x+1 problem, J. of Combinatorial Mathematics and Combinatorial Computing, 44 (2003), 177–187. (MR 2004a:11017)"

"Charles C. Cadogan (2006), A Solution to the 3x+1 Problem, Caribbean J. Math. Comp. Sci. 13 (2006), 1–11."

I have searched on google and have found nothing. Can anyone help?


Here two of these articles, and two others older:

Lagarias in "The 3x + 1 Problem: An Annotated Bibliography, II (2000-2009)" p.2 mentions that "The proofs claimed in […] Cadogan (2006) [… is] incomplete." An error p.7 invalidates the following and the assert of proof of the conjecture.

Note also that these several papers contain almost the same materials.

  • $\begingroup$ The second bibliography covering (2000-...) compiled by G. Lagarias contains a refutation of the attempted solution presented in Cadogan(2006) because of an error near eq (2.6) which makes the following derivations a non-sequitur. (It is not known to me, whether Cadogan has retracted his(2006) claimed proof, though.) (... and thank you very much to make these papers available at all!) $\endgroup$ Feb 12 '20 at 2:45
  • 1
    $\begingroup$ You right. I added that. $\endgroup$ Feb 12 '20 at 9:03

Apparently it is possible to request The 3x+1 problem: towards a solution to the author here: https://www.researchgate.net/publication/268028676_The_3x1_problem_towards_a_solution

EDIT: Unfortunately this mathematician died in 2015 : UWI Mourns the Passing of Renowned Mathematician, Professor Emeritus Charles Cadogan

  • $\begingroup$ Thanks, any idea on the other two? $\endgroup$
    – Roskiller
    Feb 7 '19 at 20:19
  • $\begingroup$ Maybe you can ask to the author itself by contacting him with the ResearchGate website. $\endgroup$ Feb 7 '19 at 20:21
  • $\begingroup$ Unfortunately this mathematician died in 2015: maths-et-physique.net/aberkane-syracuse.html $\endgroup$ Feb 9 '20 at 20:07

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