🚀 go-pugleaf

RetroBBS NetNews Server

Inspired by RockSolid Light RIP Retro Guy

Article View: fj.sci.math
Article #14106

Collatz problem (was: Re: [Q]koratt)

#14106
From: Yuzuru Hiraga
Date: Fri, 08 Dec 1995 00:00
55 lines
2761 bytes
$BJ?2l!w?^=q4[>pJsBg3X$G$9!#(J

In article <4a4c3l$7se@news.tech.gakken.co.jp> yamada@tech.gakken.co.jp writes:
>$B;3ED(J@$B3X=,8&5f<R$G$9!#(J "Collatz$B$NLdBj(J"$B$K$D$$$F$O(J
>
>"Unsolved Problems in Number Theory"	Richard K.Guy
>1981 Springer-Verlag		$B!JBh#2HG$,$"$k!)!K(J
>
>$B$N(JP120$B$K=q$$$F$"$j$^$9!#(J7x10^11$B$^$G$O3NG'$5$l$F$$$k$h$&$G$9!#(J
>$B$3$NCf$KJ88%%j%9%H$b=q$$$F$"$j$^$9!#(J

sci.math $B$N(J FAQ $B$K$b0J2<$N$h$&$KF1$8;XE&$,$"$j$^$9!'(J

>From: alopez-o@neumann.uwaterloo.ca (Alex Lopez-Ortiz)
>Subject: sci.math FAQ: Unsolved Problems
>Summary: Part 20 of 32, New version
>Message-ID: <DID14t.20C@undergrad.math.uwaterloo.ca>
>Date: Mon, 20 Nov 1995 21:02:53 GMT
>   
>                              UNSOLVED PROBLEMS
	...
>Collatz Problem
>   Take any natural number m > 0.
>   n : = m;
>   repeat
>   if (n is odd) then n : = 3*n + 1; else n : = n/2;
>   until (n==1)
>   
>   Conjecture 1 For all positive integers m, the program above
>   terminates.
>   The conjecture has been verified for all numbers up to 7 * 10^(11).
>References
>   Unsolved Problems in Number Theory. Richard K Guy. Springer, Problem E16.
>   Elementary Number Theory. Underwood Dudley. 2nd ed.

$B$?$@(J 7*10^11 $B$H$$$&>e8B$O$@$$$V8E$$$h$&$G!"(J
$B!!!!FqGH40<$!'!V3QC+!J$+$/$?$K!K$NLdBj!W(J
$B!!!!!J?t3X%;%_%J!<A}4)!"!V?t3X(J 100 $B$NLdBj!W(Jp.117-119$B!"F|K\I>O@<R(J, 1984$B!K(J
$B$H$$$&#1#0G/0J>eA0$N5-;v$G$b!"(J3*10^12 $B$^$G$O2r$,$J$$!JJFED?.IW;a$i$K$h$k!K(J
$B$H$J$C$F$$$^$9!#$b$A$m$s:#$G$O$b$C$H@h$^$G8!>Z$5$l$F$$$k$N$G$7$g$&!#(J

In article <WAKAMATU.95Dec7180030@parsley.kurims.kyoto-u.ac.jp>
wakamatu@kurims.kyoto-u.ac.jp (Wakamatsu Kazuhiro) writes:
>$B<c>>$G$9!#(J
>$BA0H>$NA`:n$N8e$OI,$:4q?t$G$9$+$iBg;(GD$K!"(J
>$B3NN(E*$K$$$&$H#1!?#2$N3NN($GLs#3!?#2G\!"(J
>$B#1!?#2$N3NN($G#1!?#2G\$K$J$k$o$1$G!"(J
>$B#22s$G4|BTCM!J!)!K$,Ls#3!?#4G\$K$J$k$o$1$G(J
>$BD9$$L\$G8+$l$P>.$5$/$J$C$F$$$/$7!"$^$"!"@5$7$$$@$m$&$H$$$&(J
>$B5$3Z$JOC$,$"$j$^$9!#(J

$B>e$NFqGH@h@8$N5-;v$K$b$3$l$HF1MM$NI>2A!J$?$@$7>pJsNL$G=q$+$l$F$$$k!K(J
$B$,9T$o$l$F$$$^$9!#$3$N5-;v$OC;$$$J$,$i!"B>$K$b$*$b$7$m$$OC$,=P$F$$$^$9!#(J

$B!JJ?2l!K(J
Technical Details
Message-ID: <DJABML.DBq@ulis.ac.jp>
Path: arc1-ca.pugleaf.net!unknown!not-for-mail
References: <TAKERU.95Dec4213830@metis.cse.kyutech.ac.jp> <4a4c3l$7se@news.tech.gakken.co.jp>

Show Full Headers
Complete Article Headers
X-Google-Language: Japanese,JIS
X-Google-Thread: f4956,9b8699e8e6da9a25
X-Google-Attributes: gidf4956,public
From: hiraga@ulis.ac.jp (Yuzuru Hiraga)
Subject: Collatz problem (was: Re: [Q]koratt)
Date: 1995/12/08
Message-ID: <DJABML.DBq@ulis.ac.jp>
X-Deja-AN: 121281352
distribution: fj
sender: news@ulis.ac.jp (bach Usenet News System)
references: <TAKERU.95Dec4213830@metis.cse.kyutech.ac.jp> <4a4c3l$7se@news.tech.gakken.co.jp>
organization: Univ. of Lib. & Info. Sci., Tsukuba Japan 
newsgroups: fj.sci.math