"Guessing the outcome of iterations of even most simple arithmetical functions could be an extremely hazardous experience. Not less harder, if at all possible, might be to prove the veracity of even a "sure" guess concerning iterations : this is the case of the famous $3x+1$ conjecture. Our purpose here is to study and conceptualize some intuitive insights related to the ultimate (un)solvability of this conjecture. "
Publié le : 1998-12-21
Classification:
iterations of arithmetical functions,
unsolvability,
"iterations of arithmetical functions,
Turing halting problem,
unsolvability",
11K31, 11K38,03D35,
[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
@article{hal-00129576,
author = {Belaga, Edward G.},
title = {Reflecting on the $3x+1$ Mystery. Outline of a Scenario.},
journal = {HAL},
volume = {1998},
number = {0},
year = {1998},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00129576}
}
Belaga, Edward G. Reflecting on the $3x+1$ Mystery. Outline of a Scenario.. HAL, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/hal-00129576/