ޥ
ࡢäȴñ...orz

Ȥꤢ⤦äȤǵ𤷤ޤޤŻʤΤ...(^^;;
PowerBook G4 1215ڡ 0:03:35 MAIL:masaru-y@sansu.org HomePage:26327
2709
ߣ/ǣ
̤

ѥˤޤäƤ롡 1215ڡ 0:27:22 26328
Ϥʤ
ס˲
ʤۤɡȻפޤͭ̾ʤΤ⤷ޤ󤬡ڤǤ͢
1215ڡ 0:08:37 26329
Taro
ż֤ƣˤޤˤޤǤorz
003 1215ڡ 0:08:40 26330
tomh
ʬʬҤ¤ƱʤǤ͡
ԡ 1215ڡ 0:09:55 MAIL:tomh@yahoo.co.jp HomePage:H to M26331
ҥǡ
ΤȤ˥ꥢ륿໲äǤƥåǤ
餱櫓ˤϤޤ󤷡
1215ڡ 0:10:38 26332
2709
ޤˤϾ˲֤
ѥˤޤäƤ롡 1215ڡ 0:15:08 26333
̵
ǤդXɽεտɽ
ʬʬǤդXƱˤʤʬҤ礭˽ɽΤƱ֤ˤʤ뤳Ȥ˵Ť

äơεտ¤ʬʬҤ1344Ǥ롣
16/51344/XɽȤX1344165420Ȥʤ롣
ʬʬǤꡢƱǤ롣
ä420Ȥʤ롣
1215ڡ 0:20:31 MAIL:akkk@hi-net.ne.jp 26334
Ȥ
Ͽ mupad light 2.5.3 Υץߥ󥰤¤1344
ʤΤƬ420ȤʤäƤ褫äȤ
i := 1: x :=1000:
for i from 1 to x do
if numlib::sumdivisors(i)=1344 then print(i) end_if;
end_for;
¹Ԥ
420
546
564
620
644
764
806
861
897
NIL
ǽ420󤵤
numlib::divisors(420);
[1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84,105, 140, 210, 420]
­
1+1/2+1/3+1/4+1/5+1/6+1/7+1/10+1/12+1/14+1/15+1/20+1/21+1/28+1/30+1/35+1/42+1/60+1/70+1/84+1/105+1/140+1/210+1/420;16/5
դɤ
420()
˭ԡ 1215ڡ 1:32:17 MAIL:fttnm528@ybb.ne.jp 26335
uchinyan
ϤϤ褦ޤ䤵Ǥ ^^/
εտ¤ϡʬȡʬϸˡʬҤϤ礦ɸ¤ˤʤޤݥȤϤ
ǡ1344/16 = 84 ʤΤǡ16/5 = (16 * 84)/(5 * 84) = 1344/420 Ȥʤꡢ 420 Ǥ
ͥνȡ 1215ڡ 8:45:21 MAIL:uchi@sco.bekkoame.ne.jp 26336
uchinyan
Ǽɤߤޤޤ礷äϤʤ褦Ǥ
ϡΡȻפäƤΤǤ ^^:
ͥνȡ 1215ڡ 8:57:02 MAIL:uchi@sco.bekkoame.ne.jp 26337
kasama
Ϥ褦ޤ(*^_^*)

Question481()=
{
local(n,ds,i,s);
n = 1;
while (true,
ds = divisors(n);
s = 0;
for (i=1,length(ds), s += ds[i]);
if (s == 1344,
s = 0;
for (i=1,length(ds), s += 1/ds[i]);
if (s == 16/5,
print(n);
break;
);
);
n++;
);
}
1215ڡ 9:24:42 26338

uchinyanΤȤ˵ŤΤˣʬޤñǻƤˡ§򸫤ĤɤȤȤ򼨤ƤǤ͡
1215ڡ 10:42:03 26339
ϥ饮㡼ƥ
MathematicaǤDivisorsȤTotalȤ̿Ǵñ
׻Ǥޤ
̶彣 1215ڡ 10:43:10 HomePage:ĩ26340
ϥ饮㡼ƥ
Ԥ˥ʸǽ񤫤줿̾ޤˤ
ǯںߤΤǥʸǤ
̶彣 1215ڡ 11:10:44 HomePage:ĩ26341
粬ҹ
ʹףˡʹף
ʹףˡʹףˤǤϲʬΤޤޤʬ䤹Ǥʡ
ιפտιפʬҤˤʤäƤꡢʬ줬Ȥοȸͽۤޤ
ءᣱäƣءᣴ
ߤ꤬Ϥ䤹Ǥ͡ʡ
ˤƤ⣱̤λ֤Ǥ͡ޤ˽ֻʶá
1215ڡ 14:01:04 MAIL:toshi009@land.hokuriku.ne.jp 26342

äѤꤽǤ礦ࣱ᣸ߣǤ͡ǧΤ˽Ф٤­Ƥߤޤ衦
1215ڡ 14:25:44 26343
???
ʬ׻äubasic
10 'asave "sc481.ub"
20 Max=1344
30 for N=1 to Max
40 Wa1=0
50 Wa2=0//1
55 J=1
60 while and{J<=N,Wa1<=1344,Wa2<=16//5}
70 if N@J=0 then Wa1+=J:Wa2+=1//J
80 J+=1
90 wend
100 if and{Wa1=1344,Wa2=16//5} then print N
110 next N
120 end
1215ڡ 15:27:09 26344
⡼ޥ
ʤĤñä
Ȥȡ
1+x1+x2++m/x2+m/x1+m=1344
1+1/x1+1/x2++x2/m+x1/m+1/m=16/5
Ĥޤꡢ1651344äƤȡʤΤǡ
420
ΤȤϰŪ˸뤳ȤǤ͡
1215ڡ 20:31:13 MAIL:kennji72001@yahoo.co.jp 26345
uchinyan
ưפǤĥͤƤߤޤϡ񤷤Ǥ
ޤ¤ 1344 Ȥ̵ˤƤߤޤ16/5 ϤΤޤޤǤΤȤϡ
perl Ĵ٤Ƥߤޤʥ֤ʥǥ󥰤ʤΤǡΨϤ褯ޤ󤬡

# Sansuu Challenge 481

$n = 100000;
$p = 16; $q = 5;

sub divSum {
local($a) = @_; local($s) = 0;
foreach (1..$a/2) {
$s += $_ if($a % $_ == 0);
}
$s += $a;
return($s);
}

print "$n ޤǤη̡\n";
foreach (1..$n) {
$s = &divSum($_);
if($p * $_ / $q == $s) {
print "$p/$q $_, $s\n";
}
}

̤ϡΤȤꡣ򸫤ȡʣ褦Ǥ

100000 ޤǤη̡
16/5 420, 1344
16/5 7440, 23808
16/5 8190, 26208
16/5 18600, 59520

ʤμϡ

16/5 121920, 390144

Ȥʤ褦Ǥθ夬ʤʤĤޤ
ϡθĿͭ¤ɤͭ¤ʤдĤ뤫ŪˤΤȤϤʤˤʤɤǤ
ǤϤ褯ʬäƤޤ
ޤ褯ʬäƤʤΤǤεտ¤μͤϰϤϤɤʤäƤ뤫
ʬ뤳Ȥϡ
ͭǤ뤳ȡ
1 ʾǤ뤳ȡϡ 1 ͤʬޤ
¤Ϥʤȡϡ㤨С n! 1 + 1/2 + 1/3 + ... + 1/n n -> ̵ˤʤ뤳Ȥʬޤ
ξ 2 Ȥʤ뤳ȡȤϡ󡢼ʬȤ¤οʤΤȤǤ
פϡ1 ʾͭǡͤϰϤǤ뤫ɤǤ
ͥνȡ 1215ڡ 21:13:08 MAIL:uchi@sco.bekkoame.ne.jp 26346
พี่ชุณ(ԡ)
#26341

ͤǤ

#25001

ǯĹˤؼκݤΥڡ򸫤ĤĹˤ᤿ΤǤΤۤϤޤäƤޤǯܲϢǤ֥ϥ饮㡼ƥפΤ̾ҸƤޤ
Ĺˤ̾ڤƤޤ&#3614;&#3637;&#3656;&#3594;&#3640;&#3603;(ԡ)פȤϥǡ֥󷻤פȤ̣Ǥ
ȤɤԤˡ֥ξݤפȤ̾򸫤⤷ȻƱпȤΤʤȻפ̾򥿥ʸˤƤߤޤ
Ȥꤤޤ

ȤǺǤʲΤ褦˹ͤޤޤ껻餷ޤ󤬡ͤޤǡ
᤿aȤa = (p1^n1)*(p2^n2)*ĤȤޤ
a = (1+p1+p1^2++p1^n1)*(1+p2+p2^2++p2^n2)* = 1344Ȥʤޤ
aεտ = (1+1/p1+1/p1^2++1/p1^n1)*(1+1/p2+1/p2^2++1/p2^n2)*
= ((1+p1+p1^2++p1^n1)/p1^n1)*((1+p2+p2^2++p2^n2)/p2^n2)*
= ((1+p1+p1^2++p1^n1)*(1+p2+p2^2++p2^n2)*)/((p1^n1)*(p2^n2)*)
= ((1+p1+p1^2++p1^n1)*(1+p2+p2^2++p2^n2)*)/a
= 1344/a
äơ16/5 = 1344/a
a = 1344*5/16 = 420
Ūعʬ褦ˡʤǤ礦
1215ڡ 21:39:21 26347
monkey business
Ϥޤơ
錄Τäˡϡ
ƤΡεտפʬʬϵ᤿ʣˤˤʤꡢʬҤϡƤפ­¨1344ˤʤΤǡ1344/=16/5
äơ=1344*5/16=420Ȥʤ롣
ȤʤȤŤ餤ˡǤޤԡ󤵤٤ȡʤդʤ^^;
1215ڡ 22:37:32 MAIL:gone-going@ezweb.ne.jp 26348
ȥȥ
ˤ뤫Ĵ򤯤ƤäȿƤޤ
ޤ˵Ƥ⿩򤷤鿲η֤
äȾǤΤ˥󥸤Ƥߤޤ
ʼ˸лԡ 1216ʶ 16:28:11 MAIL:h-sakai@zb3.so-net.ne.jp 26349
ʥե
Ϥϡmonkey businessΤդʤ顢ƱǤʡ
쥬Ȥ˲򤱤ФǤ
1216ʶ 21:07:12 26350
y.kobayashi
տ¤ʬΣäƤΤ飵ܿʡȻפƣ­ʤäΤǾ䤷Ƥä顢ĤޤꣴȻԺƤäĤޤФʤ꤫Ǥ͡Ϥ
1216ʶ 21:23:54 26351
พี่ชุณ(ԡ)
#26346

uchinyanγĥ꤬򤽤äΤǾͤƤߤޤ
θĿŪʹˡϤޤ狼ޤ󤬡üʹˡҤȤĸĤޤ

420 = (2^2)*3*5*7
7440 = (2^4)*3*5*31
121920 = (2^6)*3*5*127

((2^n)-1)ǿ(륻ǿ n = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89 )Ǥ
a = (2^(n-1))*3*5*((2^n)-1) ˤʤޤ

n = 13 ΤȤ ((2^13)-1) = 8191 ǿˤʤꡢ a = (2^12)*3*5*8191 = 503255040
n = 17 ΤȤ ((2^17)-1) = 131071 ǿǡ a = (2^16)*3*5*131071 = 128848035840
n = 19 ΤȤ ((2^19)-1) = 524287 ǿǡ a = (2^18)*3*5*524287 = 2061580369920

ϼΤ褦˾Ǥޤ
a = (1+2+(2^2)++(2^(n-1)))*(1+3)*(1+5)*(1+((2^n)-1))
= ((2^n)-1)*4*6*(2^n) = 16*a/5

륻ǿϳΤ38ĤޤdzꤷƤΤǡιˡ n = 2 37Ĥβ򸫤ĤȤˤʤޤ
1216ʶ 23:16:36 26352
uchinyan
#26352
ԡ ءδĶǤϡʸޤϤǤʤ褦ʤΤǡҤ餬 Ǥʤ
¿ʬUnicodeȤʸμλȤȤǴĥФΤǤ礦m(__)m
륻ǿȤäͻ̣ҸޤΤˤäȤǤ͡򤤡
8190 18600 ȤɽǤʤ褦ǤϡɤƤʤΤǤ礦
ΥץߥʡȤפɮǥåƤߤΤǤְäƤϤʤ褦Ǥ
ͥνȡ 1217ڡ 0:06:15 MAIL:uchi@sco.bekkoame.ne.jp 26353
⡼ޥ
ɤǤ⤤ȤǤ
̤ˤΣ¤
ʬΣ¤ΡǤΤȤƱͤˡΡǡΡʤΤǡ
躬ʣ/ΡǡˤǤ͡
1217ڡ 0:16:03 MAIL:kennji72001@yahoo.co.jp 26354
พี่ชุณ(ԡ)
#26353

uchinyanءˤʤ餺֤Ҥ餬ʡפǷ빽ǤǽΤϤҤ餬ʤΤߤǤ
륻ǿϰĤüǡʳη⤿󤢤褦Ǥ


18600 = (2^3)*3*(5^2)*31
(2^3) = 1+2+4+8 = 15 = 3*5
(2^n)¤ĤǿѤǽɽ硢οϤޤ󤬡(2^n)*(5^2)*ĤǿѤηˤʤ褦Ǥ
(2^8) = 511 = 7*73
Ȥäơ
a = (2^8)*(5^2)*7*19*31*37*73 = 71271827200
򸫤Ĥޤ
ʤο3dzڤʤȤuchinyanθĤۤȰ㤦ȤǤΤȤޤ򤬸ĤäƤޤ

ޤƤߤȲ̵¤ˤ褦˻פޤǤǤ礦
1217ڡ 7:26:22 26355
uchinyan
#26355
ʬ󵯤Ƥʤ顢ɤΤȻפäƤޤǤ򤽤ˤʤäƤޤ
ȤϤΤΡͤͤƤޤ16/5 β˴ؤơޤǤξޤȤƤߤޤ

2^n - 1 ǿ륻ǿξ硢2^(n-1) * 3 * 5 * (2^n - 1) ˤʤ롣n = 2 Ͻǡ37 Ĥβ򤬤롣
2^n * 5^2 * (ǿ) Ȥ򤬤롣ʤȤ⡢2^3 * 3 * 5^2 * 31 2^8 * 5^2 * 7 * 19 * 31 * 37 * 73 ϳǧ
ʳˡʤȤ⡢2 * 3^2 * 5 * 7 * 13 = 8190 Ȥ򤬤롣ηξܺ٤ϡޤ

ʤWikipedia򸫤¤Ǥϡ֤ϳꤷƤʤΤΡ42ĤΥ륻ǿ¸ߤΤƤ餷Ǥ
ΰ̣Ǥϡǽιܤϡ41ġ(= 42 - 1) ȤäƤ褦˻פޤ

ˡͽۤȤʤȤȤơ

륻ǿϡͭ¸Ĥ̵¸ĤʬäƤʤʳηͭ¤̵¤󤢤ꤽ
2^(n-1) * (2^n - 1) ϴ 2 Ϳ뤳ȤʬäƤΤǡǤʿ 8/5 ͿΤСˤʤ롣
2^n * 5^2 * (ǿ) Ȥ˴ؤơ2^n ¤ĤǿѤɽˤϡ򤬤뤫
βϤ뤫

2^n * 5^2 * (ǿ) ȤˤĤƤϡʤȤ⡢n = 10 ξ硢
2^10 ¤ 2^11 - 1 = 2047 = 23 * 89 ǿѤˤʤޤäȹͤǤϡޤʤ褦Ǥ

ʤ꤬ 16/5 äΤǤ˹äƤޤ 16/5 ˰̣Τ⡢褯ʬʤȤǤ
ϡԤΥޥ뤵ˤʹΤ⡣
16/5 ˤϡ̣äƽʤ줿ΤǤ礦

#26354
˻פޤפʡĤְ㤨Τ (^^;
ͥνȡ 1218 21:15:46 MAIL:uchi@sco.bekkoame.ne.jp 26356
uchinyan
#26346#26356
äȰäץ
n ¤ S(n) Ȥεտ¤ T(n) ȤȡT(n) = S(n)/n Ǥ
n = p^a * q^b * ... * r^cp, q, ..., r ǰȤȡ
S(n) = {p^(a+1) - 1}/(p - 1) * {q^(b+1) - 1}/(q - 1) * ... * {r^(c+1) - 1}/(r - 1)
ʤΤǡ
T(n) = T(p^a) * T(q^b) * ... * T(r^c)
ȤʤꡢǿΤ٤ξͤнʬʤȤʬޤ
꤬Ҳ줿櫓ǤDzʬʤʤ
ͥνȡ 1218 0:06:00 MAIL:uchi@sco.bekkoame.ne.jp 26357
⡼ޥ
#26352
򤤤ΤǤ錄ʤ˻á

a ¤ M Ȥ롣
a=5M/16
ʤΤǡa 5 ˻ġ
M ϡ1+5=6=2*3 ʤΤǡa ϡ2,3 ˻ġ
ޤa 2^4 dzΤǡ2^k (k 3ʾˤ˻ġ
Ĥޤꡢa=2^k*2*3*5*p ȤȤִñ p ǿȤȡ
M=(2^(k+2)-1)*2^3*3*(1+p) ʤΤǡ
a=2^k*2*3*5*p=5M/16=5*(2^(k+2)-1)*2^3*3*(1+p)/2^4 ʤΤǡ
2^k*p=(2^(k+2)-1)*(1+p)/2^2
Ĥޤꡢ2^(k+2)*p=(2^(k+2)-1)*(1+p) ʤΤǡ
2^(k+2)-1=p ǤФ
p ϡ륻̿

a 5^2 ǰ˻ĤȤϤ褯ʬʤ
1218 18:03:47 MAIL:kennji72001@yahoo.co.jp 26358
DrK
ˤĤƤϡʿʳ2оݤˤʤΤ¸ߤ롣
ΤȤ˵ŤСñǤ͡
¤εտ¤ФٸοܤˤʤäƤ뤳Ȥ狼ФƱ͡
1336/(16/5)=420
٤Ͼγڱࡡ 1218 19:30:04 MAIL:satoka@star.odn.ne.jp 26359
DrK
#26359
1336ʤ1344Ǥ
᤯Τǥꥢ륿ǤϤޤǤ
٤Ͼγڱࡡ 1218 19:35:09 MAIL:satoka@star.odn.ne.jp 26360
Ҷ˥ޥ˥ޥ繥
Ķñ!21ޤǤ44!ϤԤ!1ޤǤ1äƤޤ!
ӤʤƥѥǤ 1219ʷ 17:23:52 26361
uchinyan
#26346, #26356, #26352, #26358 ʤɡ
θ塢ƥޥƥå˲õˡͤ餤ǡǰʤ餢ޤŸϤޤ
־פȤΤϡˡ¿Τǡʤޤ
פˡ르ꥺˤϤʤäƤʤȤȤǤ
޳ѹͤΤǡĹʤޤޤȤƤޤ

ݥȤϡ#26357ΰҲ()ʬ򡢤Ǥ
μ顢ʬ˿ĤäƤˤϡǰ򸵤οǰ˴ޤळȤʬޤ
̤ƹͤƤߤޤ
T(n) = 16/5 ʤΤǡn 5 ǰˤޤ 5 ΰ 5^1 Ǥä 5^2 ʤɤǤϤʤȲꤹȡ
T(5) = 6/5 Ȥʤꡢ16/5 = T(n) = T(5) * T(Ĥ) = 6/5 * T(Ĥ) ʤΤǡT(Ĥ) = 16/5 * 5/6 = 8/3 Ǥ
Ǻ٤ 3 ǰˤޤ3^1 Ȳꤹ T(3) = 4/3 ǡĤϡ8/3 * 3/4 = 2 Ǥ
2 ͿΤϴʤΤǡ2^n - 1 ǿΤȤ2^(n-1) * (2^n - 1) ˤʤޤ
n = 2 ϡ3 ˤäƤޤۤɤ 3^1 β̷⤹Τǽޤ
򡢼Τ褦˽񤯤Ȥˤޤ

16/5
5 : 1 + 5 = 6, 6/5
16/5 * 5/6 = 8/3
3 : 1 + 3 = 4, 4/3
8/3 * 3/4 = 2
2 : ... () ...
2^(n-1) * (2^n - 1)
--->
2^(n-1) * 3 * 5 * (2^n - 1)

2 β˴ؤ...פϡϷ׻³Ȥ̣Ƥޤ
η׻ϡʬ줬 1 ʤΤǡ¤ϡºݤ˹ԤΤ񤷤ʤޤ
ǰȤʤ٤ǿʬƤޤäƤΤǡŬ䤦ޤ
㤨С2 2^1 Ȳꤹȡ

16/5
5 : 1 + 5 = 6, 6/5
16/5 * 5/6 = 8/3
3 : 1 + 3 = 4, 4/3
8/3 * 3/4 = 2 = 4/2
2 : 1 + 2 = 3, 3/2
4/2 * 2/3 = 4/3
--->
NG

Ǹʬη׻ 4/3 ˤʤꡢ 3^1 Ȳꤷǰ 3 ƤӸޤ̷Ǥ
NG ϼԤȤɽޤʤϡξ n = 2ޤʤ硢бƤޤ
Ԥ硢бȤơ2^2 Ȳꤹ롢2 ʳǿͤ롢Ĥˡޤ
Ԥϡ3, 5 ϴ˽ФƤΤǡ7 оݤˤʤޤɤ餬ȽǤϡǰʤ顢褯ʬޤ
괺2^2 ȤƤߤȡ

16/5
5 : 1 + 5 = 6, 6/5
16/5 * 5/6 = 8/3
3 : 1 + 3 = 4, 4/3
8/3 * 3/4 = 2 = 4/2
2^2 : 1 + 2 + 2^2 = 1 + 2 + 4 = 7, 7/2^2 = 7/4
4/2 * 4/7 = 8/7
7 : 1 + 7 = 8, 8/7
8/7 * 7/8 = 1
--->
2^2 * 3 * 5 * 7

ǡޤޤϡξ n = 3 бޤ7 ⤦ޤ˽ФƤƤޤ
ƱͤΤȤ򷫤֤ơ¾βõȤϲǽǤ꤬ʤΤǡϤޤǤˤƤޤ
ββǽȤƤϡ3 3^1 ǤϤʤ 3^2 Ȳꤹ礬ޤϡ

16/5
5 : 1 + 5 = 6, 6/5
16/5 * 5/6 = 8/3
3^2 : 1 + 3 + 3^2 = 1 + 3 + 9 = 13, 13/3^2 = 13/9
8/3 * 9/13 = 24/13
13 : 1 + 13 = 14, 14/13
24/13 * 13/14 = 24/14 = 12/7
7 : 1 + 7 = 8, 8/7
12/7 * 7/8 = 12/8 = 3/2
2 : 1 + 2 = 3, 3/2
3/2 * 2/3 = 1
--->
2 * 3^2 * 5 * 7 * 13

Ȥʤäơ2 * 3^2 * 5 * 7 * 13 = 8190 βͿޤʤθǤ2^2 Ϲͤʤ OK Ǥϡ
2^2 : 1 + 2 + 2^2 = 1 + 2 + 4 = 7, 7/2^2 = 7/4
3/2 * 4/7 = 6/7 < 1
ʤΤǡT(n) >= 1 ̷⤹뤫ǤϾˤޤ
򤬵ޤˤϺǸʬ 1 ˤʤޤΤȤǰ p^k ΤȤp^(k+m), m > 0 Фơ
T(p^k) = (1 + p + ... + p^k)/p^k = 1 + 1/p + ... + (1/p)^k
T(p^(k+m)) = (1 + p + ... + p^k + ... + p^(k+m))/p^(k+m) = 1 + 1/p + ... + (1/p)^k + ... + (1/p)^(k+m)
ʤΤǡT(p^k) < T(p^(k+m)) ǤǸʬ N/T(p^k) = 1 ȤʤäƤΤǡN/T(p^(k+m)) < 1 Ȥʤ̷Ǥ
Ĥޤꡢ򤬸Ĥäǰ˴ؤƤϡʾͤɬפϤʤȤȤǤ
ޤ١1 꾮ʤС礭ʥ٥˴ؤƤϡ 1 꾮ʤΤǡͤɬפϤޤ
ߤ˴ؤơޤǤʬäƤޤȤƤȡ
򤬸Ĥä硣
˲ꤷǰƤʬ˸줿硣ϡԤǤ
Ĥʬ 1 꾮ˤʤä硣⡢ԤǤ
ʾθơۤɤ³Ԥäơ¾βõƤߤޤ

16/5
5 : 1 + 5 = 6, 6/5
16/5 * 5/6 = 8/3
3^2 : 1 + 3 + 3^2 = 1 + 3 + 9 = 13, 13/3^2 = 13/9
8/3 * 9/13 = 24/13
13 : 1 + 13 = 14, 14/13
24/13 * 13/14 = 24/14 = 12/7
7^2 : 1 + 7 + 7^2 = 1 + 7 + 49 = 57 = 3 * 19, (3 * 19)/7^2
12/7 * 7^2/(3 * 19) = (4 * 7)/19
19 : 1 + 19 = 20 = 2^2 * 5, (2^2 * 5)/19
(4 * 7)/19 * 19/(2^2 * 5) = 7/5<----- 5 и
--->
NG

16/5
5 : 1 + 5 = 6, 6/5
16/5 * 5/6 = 8/3
3^2 : 1 + 3 + 3^2 = 1 + 3 + 9 = 13, 13/3^2 = 13/9
8/3 * 9/13 = 24/13
13 : 1 + 13 = 14, 14/13
24/13 * 13/14 = 24/14 = 12/7
7^2 : 1 + 7 + 7^2 = 1 + 7 + 49 = 57 = 3 * 19, (3 * 19)/7^2
12/7 * 7^2/(3 * 19) = (4 * 7)/19
19^2 : 1 + 19 + 19^2 = 1 + 19 + 361 = 381 = 3 * 127, (3 * 127)/19^2
(4 * 7)/19 * 19^2/(3 * 127) = (4 * 7 * 19)/(3 * 127)<----- 3 и
--->
NG

16/5
5 : 1 + 5 = 6, 6/5
16/5 * 5/6 = 8/3
3^2 : 1 + 3 + 3^2 = 1 + 3 + 9 = 13, 13/3^2 = 13/9
8/3 * 9/13 = 24/13
13 : 1 + 13 = 14, 14/13
24/13 * 13/14 = 24/14 = 12/7
7^2 : 1 + 7 + 7^2 = 1 + 7 + 49 = 57 = 3 * 19, (3 * 19)/7^2
12/7 * 7^2/(3 * 19) = (4 * 7)/19
19^3 : 1 + 19 + 19^2 + 19^3 = 1 + 19 + 361 + 6859 = 7240 = 2^3 * 5 * 181, (2^3 * 5 * 181)/19^3
(4 * 7)/19 * 19^3/(2^3 * 5 * 181) = (7 * 19^2)/(2 * 5 * 181)<----- 5 и
--->
NG
...

ȡNG ³ޤ19^k η󤬽ꤽˤޤ󡣤줬԰¤ȤäͳǤ
ʤ⤷5 ΰ 5^2 ˤ顢Ϥ椬ǤʤȤ⡢

16/5
5^2 : 1 + 5 + 5^2 = 1 + 5 + 25 = 31, 31/5^2
16/5 * 5^2/31 = (16 * 5)/31
31 : 1 + 31 = 32 = 2^5, 2^5/31
(16 * 5)/31 * 31/2^5 = 5/2
2 : 1 + 2 = 3, 3/2
5/2 * 2/3 = 5/3
3 : 1 + 3 = 4 = 2^2, 2^2/3
5/3 * 3/2^2 = 5/2^2
--->
NG
...

16/5
5^2 : 1 + 5 + 5^2 = 1 + 5 + 25 = 31, 31/5^2
16/5 * 5^2/31 = (16 * 5)/31
31 : 1 + 31 = 32 = 2^5, 2^5/31
(16 * 5)/31 * 31/2^5 = 5/2
2^2 : 1 + 2 + 2^2 = 1 + 2 + 4 = 7, 7/2
5/2 * 2/7 = 5/7
7 : 1 + 7 = 8 = 2^3, 2^3/7
5/7 * 7/2^3 = 5/2^3
--->
NG
...

16/5
5^2 : 1 + 5 + 5^2 = 1 + 5 + 25 = 31, 31/5^2
16/5 * 5^2/31 = (16 * 5)/31
31 : 1 + 31 = 32 = 2^5, 2^5/31
(16 * 5)/31 * 31/2^5 = 5/2
2^3 : 1 + 2 + 2^2 + 2^3 = 1 + 2 + 4 + 8 = 15 = 3 * 5, (3 * 5)/2^3
5/2 * 2^3/(3 * 5) = 2^2/3
3 : 1 + 3 = 4 = 2^2, 2^2/3
2^2/3 * 3/2^2 = 1
--->
2^3 * 3 * 5^2 * 31
...

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ͥνȡ 1219ʷ 21:16:01 MAIL:uchi@sco.bekkoame.ne.jp 26362