Abstract
The 3 x + 1 semigroup is the multiplicative semigroup S of positive rational numbers generated by { 2 k + 1 3 k + 2 : k ⩾ 0 } together with { 2 } . This semigroup encodes backwards iteration under the 3 x + 1 map, and the 3 x + 1 conjecture implies that it contains every positive integer. This semigroup is proved to be the set of positive rationals a b in lowest terms with b ≢ 0 ( mod 3 ) , and so contains all positive integers.
Full Text 
Sign-in/Register to access full text options
Sign-in/Register to access full text options 
Published version (
Free)
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
