
Re: seq question again
Posted:
Oct 6, 2009 7:14 AM


Am 06.10.2009 10:31 schrieb Gottfried Helms: > Am 06.10.2009 03:20 schrieb leiko: >> On Oct 5, 6:50 pm, er...@sfu.ca (Erick Bryce Wong) wrote: >>> leiko <leikomats...@gmail.com> wrote: >>>> Gerry <ge...@math.mq.edu.au> wrote: >>>>>>>> leiko wrote: >>>>>>>>> hello everyone, I posted this a while ago, but no one responded, so i >>>>>>>>> thought I should give it another try because probably not everyone has >>>>>>>>> seen the earlier post. >>>>>>>>> If we have a recursion x_1=2, x_n=2^(x_n1), how does one show that >>>>>>>>> the sequence x_n(mod m) stabilizes in Z/mZ for any m ?
There is an article in Journal of integers
> INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 7 (2007), #A23 > ITERATED EXPONENTS IN NUMBER THEORY > Daniel B. Shapiro > Department of Mathematics, Ohio State University, Columbus, OH 43210 > shapiro@math.ohiostate.edu > S. David Shapiro > 1616 Lexington Ave #D, El Cerrito, CA 94530 > gavelmaven@aol.com
online, which is interesting for this.
It begins (sorry, no formatting here)
http://www.westga.edu/~integers/vol7.html Entry A23: > Abstract > We show that if a1, a2, a3, . . . is a sequence of positive integers and k is > given, then the sequence a1, a1^a2, a1^a2^a3 ... becomes constant when reduced (mod k). > We also consider the sequence 1^1, 2^2, 3^3, . . . (mod k), showing that this sequence, > and related ones like n^n^n (mod k), are eventually periodic. > ?Dedicated to the memory of Prof. Arnold Ross
Gottfried Helms

