The 3x+1 Semigroup

Details The 3x+1 Semigroup The 3x+1 Semigroup

2004-11-07

arxiv.org/abs/math/0411140v2

Journal of Number Theory 117 (2006), 147--159.

Mathematics

Number Theory

16 pages, latex; minor changes

Scientific paper

The 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.

Affiliated with

Also associated with

No associations

Rating

The 3x+1 Semigroup does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The 3x+1 Semigroup, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The 3x+1 Semigroup will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-25254