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Article #65

Re: another math puzzle :-)

#65
From: Seiji Kaneko
Date: Tue, 14 Apr 1992 18:18
66 lines
2980 bytes
$@$+$M$3!w$R$?$A$G$9!#MpF~!#(J
>>>>> On 13 Apr 92 02:24:50 GMT, tacchan@flab.fujitsu.co.jp (Tatsuo KONDO who is (^.^)) said:
|> $@$d$C$H$3$5%(%l%,%s%H!J$+!)(JB-$@!K$J2rEz$r8+$D$1$?$N$G4r$7$/$J$C$F(J$@%]%9%H$9(J
|> $@$k6aF#!wIY;NDL8&$G$9!#(J
|> $@Ld!'(J
|> m, n $@$O<+A3?t$G!"(J0 < m^(1/3) - n < 10^(-3) $@$rK~$?$9!#(J
|> $@$3$N$h$&$J(J m $@$,B8:_$9$k:G>.$N(J n $@$O$$$/$D$+!#(J
|> $@!JCm!'=PE5$G$O?tCM$N$_$r2rEz$9$l$PNI$$$h$&$G$7$?$,!"(J$@$3$3$G$O2rEz<j=g$b(J
|>       $@Ld$$$^$9(J:-P$@!K(J

n=19$@$G$9$+!)(J $@$J$s$+8m2r$7$F$$$k$N$+!"$=$l$@$H0W$7$9$.$kMM$J(J
$@5$$,$9$k$N$G$9$,!#8^J,$/$i$$$GJ,$+$C$F$7$^$C$?!#0J2<$O!"13(J
$@$+$bCN$l$J$$$N$G!"$=$N$D$b$j$G!#(J

$@!t(J $@2<$N(J$@2sEz$r=q$/J}$,;~4V$,$+$+$C$?!#(J;-p



$@4JC1$N0Y!"(Jy=(m)^(1/3)$@$H$9$k!#(Jy$@$h$jBg$-$$:G>/$N<+A3?t(Jp$@$H!"(Jy
$@$h$j(J$@>.$5$$:GBg$N<+A3?t(Jq$@$r9M$($k!#EvA3$J$,$i!"(Jp = q + 1
p^3$@$b(Jq^3$@$b<+A3?t$G$"$j!"(J

q^3 < m < (q+1)^3

$@$G$"$k(J$@$O$:!#0lJ}!"Bj0U$+$i!"(Jm$@$O<+A3?t$N#3>h$K6a$/6O$+$KBg$-(J
$@$$@0?t$G$"$j!"$3$3$G$O:G>/$N(Jm$@$r$b5a$a$F$$$k$O$:(J$@$G$"$k$+$i!"(J
m = q^3 + 1$@$G$"$k$H$7$F$h$$!#(J

$@!t(J y = x^(1/3)$@$N4X?t$N@-<A$+$i!">e$OL@$i$+!#(J

$@$=$3$G!"(Jm = q^3 +1 $@$H$9$k!#$3$N8+CO$+$i!":G=i$N<0$r=q$-D>$9$H!"(J
q = n $@$G$"$j(J

0 < (m)^(1/3)- (m-1)^(1/3) < 10^(-3)

$@$3$N<0$r$^$H$b$K2r$$$F$b$$$$$,!"(Jy = x^(1/3)$@$r9M$($k$H!">e(J
$@$NITEy<0$NCf1{$N9`$O$3$N4X?t$N(Jx = m$@$KCV(J$@$1$k@\@~$N79$-$h$j(J
$@6O$+$KBg$-$/!"$+$D(Jm$@$,==J,$KBg$-$$0Y$[$\Ey$7$$!#6a;w$N0Y!"(J
$@@\@~$KCV$-49$($F>e5-4X?t(J$@$rHyJ,$9$k$H(J

0 < (1/3) * m^(-2/3) < 10^(-3)

$@$rF@$k!#$3$l$rE83+$9$k$H(J m > 6085.xxx$@$rF@$k!#(J18^3 = 5832,
19^3 = 6859 $@$G$"$k$+$i!"(J6860$@$NN)K!:,$r5a$a$k$H3N$+$K(J

(6860)^(1/3) = 19.00092332xxx

$@$G$"$j!"5a$a$k(J$@>r7o$r8+$?$7$F$$$k!#$^$?!"(J18^3 + 1$@$NN)J}:,(J
$@$r5a$a$k$H(J

18^3+1 = 5833; (5833)^(1/3) = 18.00102875xxx

$@$H$J$j!"3N$+$K(Jn = 19$@$,:G>/$HJ,$+$k!#(J

$@!t(J $@$"$$$@$O$A$g$C$HHtLv$,$"$k$+$bCN$l$J$$!#B>$N?M$,Kd$a$F(J
$@!t(J $@$/(J$@$l$k$G$7$g$&!#(J

$@F1MM$N5DO@$G<B$O(J

0 < | m ^(1/3) - n | < 10^(-3)

$@$rK~$?$9(Jm,n$@$b(Jn=19$@$,:G>/$G$"$k$3$H$,(J$@J,$+$k!#$3$N$H$-$O(Jm=6858

--
Seiji Kaneko  kaneko@icsi.Berkeley.EDU,kaneko@sdl.hitachi.co.jp
..................................... 76270.2466@compuserve.com
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Message-ID: <KANEKO.92Apr14181843@axiom.icsi.Berkeley>
Path: arc1-ca.pugleaf.net!sparky!uunet!stanford.edu!agate!agate!kaneko
References: <TACCHAN.92Apr13112450@topor.soft.flab.fujitsu.co.jp>

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Path: arc1-ca.pugleaf.net!sparky!uunet!stanford.edu!agate!agate!kaneko
From: kaneko@icsi.Berkeley.EDU (Seiji Kaneko)
Newsgroups: fj.sci.math
Subject: Re: another math puzzle :-)
Date: 14 Apr 92 18:18:43
Organization: International Computer Science Institute
Lines: 66
Distribution: fj
Message-ID: <KANEKO.92Apr14181843@axiom.icsi.Berkeley>
References: <TACCHAN.92Apr13112450@topor.soft.flab.fujitsu.co.jp>
NNTP-Posting-Host: axiom.icsi.berkeley.edu
In-reply-to: tacchan@flab.fujitsu.co.jp's message of 13 Apr 92 02:24:50 GMT