Autor:	Marc Chamberland
Rok vydání:	2015
Předmět:	Discrete mathematics Algebra and Number Theory Conjecture Montel's theorem Iterated function Structure (category theory) Generating function (physics) Mathematics Collatz conjecture
Zdroj:	Journal of Number Theory. 148:384-397
ISSN:	0022-314X
DOI:	10.1016/j.jnt.2014.09.024
Popis:	The 3 x + 1 problem has resisted analysis from multiple perspectives for many decades. This paper studies the more general q x + r problem, where q and r are odd, and finds new, averaging structures for the iterates. This structure supports the conjecture that all orbits enter a cycle if q = 1 , 3 but divergent orbits exist if q ≥ 5 .
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::47f49b070bc39d41bff712a198e3097a https://doi.org/10.1016/j.jnt.2014.09.024 Zobrazit plný text záznamu Full Text from ScienceDirect