The 3x+1 Semigroup

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dc.creatorApplegate, David
dc.creatorLagarias, Jeffrey C.
dc.date2004-11-07
dc.date2005-05-04
dc.date.accessioned2026-07-07T06:31:25Z
dc.date.available2026-07-07T06:31:25Z
dc.descriptionThe 3x+1 semigroup is the multiplicative semigroup generated by the rational numbers of form (2k+1)/(3k+2) for non-negative k, together with 2. This semigroup encodes backward iteration under the 3x+1 map, and the 3x+1 conjecture implies that it contains every positive integer. We prove this is the case, and show that this semigroup consists of all positive rational numbers a/b such that 3 does not divide b.
dc.description16 pages, latex; minor changes
dc.identifierhttps://arxiv.org/abs/math/0411140
dc.identifierhttp://arxiv.org/abs/math/0411140
dc.identifierJournal of Number Theory 117 (2006), 147--159.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98597
dc.subjectNumber Theory
dc.subjectDynamical Systems
dc.subject11B83
dc.titleThe 3x+1 Semigroup
dc.typetext

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