ѥ
괺񤭽Фޤn!ǰ󤷤ФƤʤΤФΤȹͤơ15ˤɤ夭ޤ
91ڡ 0:20:57 25682
tomh
17ܰʾκȤȴȡ17ʿʤ.
13ܰʾκȤ򤹤٤Ƥȡ13ʿʤ.
äơ14,15,16ܤΤŤ줫.

3ܿͤȡϰ3145ĤϤ
Ȥ1ȤФĤˤʤäȤˤʤΤǡ
35IJä15ܤ16ܤ.
Ʊ2ܿͤȡϰ2225ĤϤ
Ȥ1ȤФĤˤʤäȤˤʤΤǡ
27IJä14ܤ15ܤ.

äơ15ܤ.

ԡ 91ڡ 0:25:31 MAIL:tomh@yahoo.co.jp HomePage:H to M25683

ͤ⣱ΣĤˤܤꤳߤͤƤޤǤ⡢ĤΤˤֻ֤ޤ
91ڡ 0:45:18 25684

30ܤޤǤκȤĤĤʤȰθĿ
30ġ29ġ28ġάˡ29ģġ30ģġȤʤ
ĤοϤʿˤʤΤǴĤˤʤ246830Ф
ˤ椫ʿˤʤȤ߹碌ӽФȺǽŪˣ1113Ĥޤ
餬ʤʤΤǡǤ13ܤϳμ¤ˤʤ겾13ܤФȤ
13ܡ12345678910111213ʿȤ߹碌ϳΤ371113äƾ51113ȹʤΤŬ
14ܡ1234567891011121314ϳΤ231113ƱͤŬ
15ܡ123456789101112131415ϳΤ251113Ȥʤ15ܤФȤ
Τ51113Ͼäޤ2ĤäƤޤޤ

15ʤΤʡ
顼θ 91ڡ 0:47:13 HomePage:25685
ߥƥ
>25685 ˣɼ

ӡ(1)(2)(3)(4)ߡġġ(30)
Τn^2 äƤȡ51113 ĤϤ
äϤʤΤǤġġ
91ڡ 0:50:36 HomePage:ߤ25686
㡼ߡ
ǽŬѷ鵤դʤäɡ
褯ͤ15ϲǤϤޤ͡

⤷1˺ʤСǤ
(1!2!)(3!4!)ߡġ(27!28!)(29!30!)
=2(1!)^24(3!)^2ߡġ28(27!)^230(29!)^2
=(ʿ)(24ߡġ2830)=(ʿ)2^{15}15!
ʤΤǡ15ܤ˺ȡ
(ʿ)2^{15}פηˤʤꡢʿˤʤޤ
91ڡ 0:53:18 MAIL:ojamaru@amber.plala.or.jp 25687
ޥ
#25685
⤷ƥߥ...

ϡ֣פĤˤʤäƤޤ򤫤碌֣^30ʣߣߣߣߣߡˡפ

ޤä^15ä...Ф..
PowerBook G4 91ڡ 0:54:46 MAIL:masaru-y@sansu.org HomePage:25688
ޥ
ߥޥ....å­Ǥ

֣פȥǤ֣פʤ飱ܡ֣פʤ飱ܡΤ褦ˡ֣פʤ֣ܡפȤΤǤ礦䳧
PowerBook G4 91ڡ 0:56:16 MAIL:masaru-y@sansu.org HomePage:25689
ߥƥ
>25689
32ξ硢251113 ĤΤǡ16ܤǣϣǤ
15ܤǤϣǤ(16 ϤޤطʤΤǡ)
91ڡ 0:59:27 HomePage:ߤ25690
ߥƥ
>25689
28ξ硢231113 ĤΤǡ14ܤǣϣǤ
ͣΤ褦Ǥ
91ڡ 1:03:30 HomePage:ߤ25691
ڼ
ΰˤʤޤ
֣פʤ֣ܡפȤΤϡʬǤ
ʿξϣݣ
ܣʿξϣܣ˲äޤ
͡ 91ڡ 1:04:34 MAIL:iida@ae.keio.ac.jp 25692
ʤˤ
֣פʤ飱ܤȣܡ֣פʤ飱
ץǤϤʤޤ
91ڡ 1:06:17 25693
ʤˤ
֣פʤ飱ܤȣܡ֣פʤ飱
ץǤϤʤޤ
91ڡ 1:07:55 25694
y.kobayashi
̲Ϥ狼ޤ󤬡ܤȤФΤʬ򤹤ȡϴˤʤäƤΤʿǤϤʤ褦Ǥ
91ڡ 1:08:23 25696
ߤ
Τˣ󤸤ʤȤޤǤ͡
ߤɡ 91ڡ 1:08:48 25697
tomh
#25683

9ʤɤνäƤ

Ȥ櫓ǡβˡϴְ㤤Ǥ m(__)m
ԡ 91ڡ 1:11:19 MAIL:tomh@yahoo.co.jp HomePage:H to M25698
ޥ
ޤ

ηǤ¿ˤǤ򤫤ƤޤޤѿޤǤm(__)m
PowerBook G4 91ڡ 1:23:20 MAIL:masaru-y@sansu.org HomePage:25700
ߥƥ
ӡ(1!)(2!)(3!)(4!)ߡġġ(91!)(92!)
2(1!)^24(3!)^2ߡġġ92(91!)^2
(ʿ)24ߡġġ92
(ʿ)2^46(46)
(ʿ)(46)
Ǥ͡(^_^)
91ڡ 1:36:32 HomePage:ߤ25701
ڼ
ΣܤˤĤƤν񤭹ߤϺޤ
ۤɡŬʤȤˡ˽񤭹ߤޤ()
͡ 91ڡ 1:38:24 MAIL:iida@ae.keio.ac.jp 25702
ߤ
ϡ46פǤ͡
ηǼĤȤΥѥɤ15פΤޤޤˤʤäƤǤ
ߤɡ 91ڡ 1:54:17 25703
ޤ륱
οˤĤĴ٤ޤܿǡҤȤĤˤʤʤΤϡ
ΤۤΣܿʤϤҤȤġ
ܿǤϤʤǡҤȤĤˤʤΤϡ
ܿǤϤʤǡդĤΤϡ
㡢䤹ߤʤ
91ڡ 2:24:23 MAIL:take4310@mobile.email.ne.jp HomePage:ޤ륱25704
ʤ
׻ϤΤʤޥ뤵ϡΤᡦ

䤤䡣׻ǤϤФȤϡŷŪʷ׻ϤȻפޤ

4827172032094201372289953186892423851333455450031742200723050556085299448655682099017817434859522451
6836414942768375764839026465591950487122401757356467759393780886539014619969732762009527056976117026
4030089480058049920654687535741203281709717672592246617854563857774456440354795775082088120498065657
2306645222912267852667734862175964017927823268853684376481853580921057024316229389104421700493448917
9214049570165676859407296953695040490481145807831871791956718363525946409198816922531305288983704178
0450564560252198140817900292931494729505658106072890578193305909495842491622367710350657892505343574
5325170247158309848462863566506586630918031242684222474025424931312186474600677332826539807576891972
4241544329245553915353194470266587044258981681378274397358193484098689286779514765291306981040097229
1605428016428574272233216903160318676051867752761575756200799691713284755419334519213221128414216932
6327895190026986877580036684831144824737672607431519484793277768420964910797535068011404838566092670
0664755304328625408772505514510301581982796601327643698202856754844699535348529506639220599306717467
4611260508988432229901351459219650433386747540863669793324440978181810357203245713133220725360617048
5551322647400098104844261551378631661969384786648453045138832288202301748584970658500724018035335870
4326831894795307606757786343101305786419670009828364923695520498591356170370105803543847324548876615
4948122456696793238133113126049206769148971962216296414365056170160374183432300787026330534977079306
9665588588249580154093538832035402300371236566969909453528147717042856181890179725643763746352478967
4228114388577876755068855909400898466718582144743727693965782342542792395787386958670001072016416347
1061972198042447459171709638775919529776649641548634095695950311436350396068617224297092879044276032
7520186278978579520494126063954789920879038291416924390856730303312317555028247602619639073160407217
5359145136042043075631047352420953207831139274605857950961448845766189735905851319804498619587646701
0622668825093463468347983424018448368345283587994691361582705475075211260933192143759195327360871714
9085602431001056472964553825279393550112012117446790192109549667372128528336937420519337399761424877
0007624728122403076878899840499447092674404301523987159639863136127424586337097972815848243717408299
2695274261636148625844185068641598700285692326087689105604130080053054368588301420060568764323977475
6872723173640783757207293079378778204260591452267297228020391099339577049513131219836673329419561215
7157593129261492669082005015100297422254880144297180866194449983200778043114419675682038073168856105
8802711488345873063899163044378671515840580748525489054999881878308765133389304220649854837948439650
0220969609650743203954245607325050374335727856493899318487078424558218366930128062307552408434840137
3625390201918565166386590265458733253792359263402603660819049994310937031770245609269924255353748390
4806119386067543886904681073857970003156384123881061119196408874709622528204248281245926591828998193
9538884458895121656857912966682424152390604976513966568363546521034465202340601866610675757304273033
7891243893187492635997243853969241520377032836721394568356419538390400967975981007140927040592046876
7528853457396089794654462076810042854225401041871963280372450371949820294305390381451197754167544481
4444803804849762204298489720832381626223014616321643740103290813727629987621326575314821206066304426
2432567277245045756135561017002837926057882928497500464933357371798545716541973986922463150578223615
1428582999636563114589931597562721674626641481691330557673345708606679141801458604867250852379925877
9619541667022256625460718528069779345200450393107530196785430036225877270174608798040254394826624238
5139429529392001437094993207535413293083725970452225762455161715963902324023824131974986841535441024
7407204430356572275922002722052927670859660404590350685520597462204783092330532111518581983780521145
5325695041797300836702943939740978844751983981129073611344867173958779465721795374347518499220410210
5978091830120784294725289827130463525496654403729801708085080842633507986139898667483619596032230901
7141131437641979977934340314837268050720064448825558935625228081754842947279460200940238533777738473
1649429344767410907481523388470415650663827811422803647795094437935436715034860997090607812431690041
5837255166705859499069901402056747735159262729250584906402591113848968435936467054290446476196344241
4973725678624837642243790480605784708854561445657994137732709243639686043917462495331399901317532990
0323151958204956195815006835033948575763464824292210478069149086596395900040862783557933513824687719
1347807104303611655131335527377867707355154708891870745182609217270734998228333532720419619928029350
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̹񡡡 91ڡ 2:49:31 MAIL:naka@sansu.org HomePage:naka's Home Page25705

Ϥ褦ޤ
466󢫤ߥäƤ롩486ˡʤ
ƽ 91ڡ 4:09:56 HomePage:θ줳ߤ󡪡25706
atomick
92ܤޤǤ׻̤ϡ

1'
1' 2
1' 2' 3'
1' 2' 3' 4
1' 2' 3' 4' 5'

1' 2' 3' 4' 5' 91'
1' 2' 3' 4' 5' 91' 92

Ȼѷ¤٤ѤǤ
1^92, 2^90, 3^90, , 92^0Ϥ줾ʿ顢λѷ'ĤοѤʿǤ
'ΤĤƤʤѤϡ
24ߡ92=2^46(12ߡ46)(2^46ʿ1ߡ46ʿ)
Ȥä'Ĥʤȡ

1
1' 2
1' 2' 3

1' 2' 3' 46
1' 2' 3' 46' 47'

1' 2' 3' 4' 5' 91' 92'

'ĤοѤʿǤ
äơ46ܤ12ߡ46ʤлĤοѤʿˤʤޤ
91ڡ 4:28:28 25707
ҡΤ
47ܰʾ47ޤΤŬ
43̤43ޤΤŬ
43,44,45,464̤ˤܤޤ
...43,44,4523ΰҤޤΤŬ
Ȥ櫓Dz򤬤Ȥ46...äƤȤǡʲ
9ߤ濴 91ڡ 7:28:19 HomePage:25708
ݤϤϼ
󡣤ʤ˿äΤ
ñˡࣲ򤷤ä
äѤꤪϼǼ
åѥɡ 91ڡ 8:53:46 MAIL:hopes@mba.ocn.ne.jp HomePage:ȣϣУţɤȤ٤Ϥ25709
kasama
Ϥ褦ޤ
á15(?_?;46Ǥͤ(^_^;

Question467()=
{
local(i,n,x);
for (i=1,92,
x = 1;
for (n=1,92, if (n != i, x *= n!));
if (issquare(x), print(i));
);
}
91ڡ 9:44:28 25710
ġ
ǽ顢30ޤǤΤȤäȤλפ15ϤФ(ޤäƤߤǤ...)줿Ȼפäơ餿ľ顢92
Ƥޤ....
ľƤޤ
91ڡ 10:42:03 25711
ϥ饮㡼ƥ
ɤ߰㤨49ȤޤǤǤ礭
ѷǤʤΤĹϲ˿Фȴ㤤ޤ

¾οͤExcelDz򤭤ޤ
̶彣 91ڡ 11:02:20 HomePage:ĩ25712
Ҷ˥ޥ
ñǤʤ󤫰ճ92Τ礦ȾʬǤ͡
91ڡ 15:12:53 25713
Ҷ˥ޥ
15ǤʤǤ?
91ڡ 15:14:50 25714
uchinyan
Ϥˤϡ
ϡīХХƤơä٤ޤ⡢ǤäƲ򤤤Τǡ׻ְ㤤Ϣȯ
Ǥ⡢ʤʤ򤫤äǤ
ɤʤȤ֤ȤϻפޤˡǤñʤΤǤäȡޤǤʤ(^^;
ơȤ顢n ܤη׻ϡ(n-1) ܤη׻̤ n!n γ衢򤫤Τˤʤꡢ
ɡ1! * 2! * 3! * ... * (n-1)! * n!ˤʤޤ
92ܤȡǽ̤ϡ1! * 2! * 3! * ... * 91! * 92! Ǥ
ΤɤβȴʿˤʤäΤǡɤγȴΤʿˤʤФ櫓Ǥ
ʿΥåϡ褯褦ˡǰʬ򤷤Ĵ٤ޤǰλؿˤʤäƤ礬ʿǤ
ܤˤѤʤΤǡפ򤷤ޤ
ޤȴʤȤƹͤޤоݤˤʤΤϡ91 ʲǿǤ
91 47 ǿξ
92/91 = 1 ; 1, ..., 92/47 = 1 ; 45 ʤΤǡ91 47 Ʋη׻˴ޤޤĿϡ
911ܡ90 = 0, 91ܡ92 = 1, ǽ =
891ܡ88 = 0, 89ܡ92 = 1, ǽ =

471ܡ46 = 0, 47ܡ92 = 1, ǽ =
ǽ̤˴ޤޤǿθĿʤΤǡ47ܰʾη׻ȴΤǤϡ
ɤ줫ǿθĿˤʤäƤޤʿˤʤʤΤǡȴ46ܰʲʬޤ
43 31 ξ
92/43 = 2 ; 7, ..., 92/31 = 2 ; 30 ʤΤǡ43 31 Ʋη׻ǴޤޤĿϡ
431ܡ42ܡ0, 43ܡ85ܡ1, 86ܡ92ܡ2, ǽ =

311ܡ30ܡ0, 31ܡ61ܡ1, 62ܡ92ܡ2, ǽ =
ǽ̤˴ޤޤǿθĿʤΤǡʿˤʤȴϡƲθĿ 1 ξ˸¤ޤ
ǡȴ43ܰʾ61ܰʲʬޤۤɤξȹ碌ȡȴ43ܰʾ46ܰʲǤ
29 ξ
92/29 = 3 ; 5 ʤΤǡ29 Ʋη׻ǴޤޤĿϡ
291ܡ28ܡ0, 29ܡ57ܡ1, 58ܡ86ܡ2, 87ܡ92ܡ3, ǽ =
ǽ̤˴ޤޤǿθĿʤΤǡʿˤʤȴϡƲθĿξ˸¤ޤ
ǡۤɤξȹ碌ơȴϡƱ43ܰʾ46ܰʲǤ
23 19 ξ
92/23 = 4 ; 0, 92/19 = 4 ; 16 ʤΤǡ23, 19 Ʋη׻ǴޤޤĿϡ
231ܡ22ܡ0, 23ܡ45ܡ1, 46ܡ68ܡ2, 69ܡ91ܡ3, 92ܡ4, ǽ =
191ܡ18ܡ0, 19ܡ37ܡ1, 38ܡ56ܡ2, 57ܡ75ܡ3, 76ܡ92ܡ4, ǽ =
ǽ̤˴ޤޤǿθĿʤΤǡʿˤʤȴϡƲθĿξ˸¤ޤ
ǡۤɤξȹ碌ȡȴϡ46ܤ˷Ǥ
ˤ줬򤫤ɤϡ17 ʲǿ˴ؤƤåɬפޤ
ݤʤΤǡǤϾܺ٤ϾάޤǿФϡ
171 16 or 34 50 or 68 84 : OK
1313 25 or 39 51 or ... : OK
11... or 22 32 or 44 54 or ... : OK
7... or 28 34 or 42 48 or ... : OK
5... or 45 49 or ... : OK
3... or 45 47 or ... : OK
2... or 46 47 or ... : OK
Ȥʤäơ46ܤϾޤ7 ʲǿǤϡ(ǿ)^k ΰդɬפǤ
ǡ46ܤǤա
ͥνȡ 91ڡ 21:19:42 MAIL:uchi@sco.bekkoame.ne.jp 25715
uchinyan
#2571415ܤϡǤϤʤȻפޤ衣
ͥνȡ 91ڡ 15:43:11 MAIL:uchi@sco.bekkoame.ne.jp 25716
HERO
ΤϤ٤ƶġä̵
ΤϤ٤ƴġ
äƺǸΰζΤĴ٤нʬ

٤ƶǣĤΤǤ٤Ƥ򣲤dz


Ȥ
Ĥޤꣴܤˤ

91ڡ 16:18:15 25717
HERO
ΤϤ٤ƶġä̵
ΤϤ٤ƴġ
äƺǸΰζΤĴ٤нʬ

٤ƶǣĤΤǤ٤Ƥ򣲤dz


Ȥ
Ĥޤꣴܤˤ

91ڡ 16:19:36 25718
uchinyan
ǼĤɤߤޤǽϡ30ܤޤǤäǤ͡ͽ۲15ܤäȤ櫓Ǥ
30ܤޤǤξ硢#25715λβˡǤϡ29 ǿϤơ3 ޤǤξ郎 15 16 Ǥ
2 ξξ郎6 7, 10 11, 12 13, 18 19, 20 21, 24 25, 30 ǡ­ΤʤȤʬޤ
ˤƤ⡢βˡñǤʤݤǤ
ɤʤ񤫤Ƥ褦ˡ٤礦η׻ޤȤơ(ʿ) * 2^n * n! ѷΤñǤ͡
ˤƤ⡢ޥ뤵ϡ¤϶ðŪʷ׻ǽϤääǤͤ ^^;
ͥνȡ 91ڡ 21:23:33 MAIL:uchi@sco.bekkoame.ne.jp 25719
X
ޤܡ餳ñȤΣɤäǤä󤳤ʤФʤʤ飱飲뤤ϣ飶Τɤ줫ǿܡΤǣȣδ֤˶äƣϴޤޤʤФʤʤϴޤǤϤʤäϣ˷ꤷޤϽ뤫äΤǸȾ١ʸФDZˤǸʸвޤʸФΤϻŸˤä餷ǤŤؤ򷡤äƤǤǤɥ󤤤ꡣѥ򤱤褯ͤ줽Ǥ䤹ߤʤ
91ڡ 23:32:05 25720
Ҷ˥ޥ
Τ15Ĵ٤Ƥߤ顢ʿˤʤޤǤ
91ڡ 23:50:15 25721
ʤ
̲ȾʬǤʤˤĴäĹǤ
#25704 ޤ륱󤵤󡢤³Ǥ

٤β 46/92 Τ褦ɽȤˤޤ
Τ褦ʣΤۤˡ
ºݤ˷׻Ƥߤȡʲβ¸ߤޤ

2 / 2
3 / 8
8 / 14
9 / 14
9 / 16
7 / 18
15 / 32
18 / 34
25 / 48
32 / 62
35 / 72
49 / 96
50 / 98
63 / 128
72 / 142
81 / 160
98 / 194

įȡֳΤˡפȸ뤤ĤΥפ¸
뤳Ȥ狼ޤΩͳϾάޤ

ףʴܷˡ
ۤ¿

ףʣܣˡʣܣˡݣ





ףݣ





ףݣ








ǤĤäΤ
ϡΡȴפμʿʤ餽
ʤȡҥףޤƤ롣

ǸΣ
ơϲơΥѥμϡ
mebius 92ʶ 0:22:44 MAIL:naka@sansu.org HomePage:naka's Home Page25722
ڼ
>ʤؤΥեǤ
Σܡʣˤξϡʿξϣȣݣǡʥףˡ
ܣʿξϣȣܣˤʤޤʥףˡ
Σܤξʣܣˤξϡܣϲˤʤޤ
ܣʿΣܤξˤϤ줬ˤʤޤʥףˡ
ˡܣʿξϤˤʤޤ9/14)
ܣʿǡʿΣܤξϡݣˤʤޤ(7/18)
ǸΣĤΥϡʿʿΣܤҤȤİ㤤¤Ǥǡ
売ͭϢʬˤǸƤǤ
Ĥϡ288/574289/574ȡ287/578Ǥ
͡ 92ʶ 2:51:02 MAIL:iida@ae.keio.ac.jp 25723
ʤ
#25723 ڼԤ󡢥ե꤬Ȥޤ

ΥͤʿѿǤ
Ĥޤꡢߣࣲ᣶ߣ

ףݣܣʣܣˡ



餬٤ƤΤ褦Ǥ
mebius 92ʶ 3:28:12 MAIL:naka@sansu.org HomePage:naka's Home Page25724
ڼ
ޤɽ򤷤ޤ͡
ۤɽƤޤ󤬡ȶ羮դʿѿϽƤޤ
ȤСߣᣳΤ褦ʾǤ
ϡףȤưƤޤ
͡ 92ʶ 3:40:13 MAIL:iida@ae.keio.ac.jp 25725
⡼ޥ
ǿ47ʾǤ̵ȤȤǡޤޤ
𤱤ʤ
46ΤȤְ㤨Ƶդ2׻Ƥʿˤʤ

ȤǼΥޡȤʲˡƤޤ󤫡ͧ


Ϳ줿(2n+1)դ¿ѷĺ顢3Ĥΰۤʤ
֡Ϳ줿¿ѷ濴3Ĥ
ˤޤ3ѷˤΨϤĤ
92ʶ 9:02:56 MAIL:kennji72001@yahoo.co.jp 25727
ʤ
#25727 ¿ѷ

٤ĺޤΥ᤮ȡʣĶȡ˥Ȥǡ
ɡʣܣˡ(ݣˤȤȤˤʤޤ󤫡
92ʶ 12:17:22 MAIL:naka@sansu.org 25728
⡼ޥ
#25728 ʤ󤢤꤬Ȥޤ
錄1ꤷȤΩ뻰ѷΤȤn(n+1)/2
32nC2
ǡ(n+1)/2(2n-1) ȹͤޤֻͧͤޤǤΤǡޤʬФΤ餻ޤ
ʤιͤƱʤΤʡ
92ʶ 20:00:40 MAIL:kennji72001@yahoo.co.jp 25729
ʤ
>ʤιͤƱʤΤʡ
Ϥʤ֤ƱǤ

Ƥͤ˽񤯤ȡ
δ֤η֡ФʤäĺˤθĿx,y,z Ȥȡ
x+y+z = 2n-2
ơֻѷ¿ѷ濴ɬ׽ʬ郎x<n,y<n,z<n

[n=4 ѷ] Ԥxy
y->
x=0
x=1
x=2
x=3
x=4
x=5
x=6 z=6-x-y

ǡȡΣ̤ꡣ̤ n(2n-1)
ΩΣ̤ꡣ̤ n(n+1)/2
äơ P = (n+1)/2(2n-1)
̹񡡡 92ʶ 20:38:05 MAIL:naka@sansu.org HomePage:naka's Home Page25730
monk
褯ʬʤǧڤޤ

ΥȤɿŪǤǤ͡˼Ԥοͳʤ餷ʤˤǤˡüԤγͤ»ŪͧŪǤ͡

¤ϡǯФꡢȤۥȤ˽ꤷƤޤϡҤ󤬤ĤͭλŻǤȤʤΤǤޤǤ˾郎ΤǤǽϡԤ̤ȤȤǡ̵򤷤ʤФʤޤ󡣤äƤȯԤĤΥݥȤã顢褦䤯ͭǻŻʤȤƥǤʤޤŻϤۤȤäƤޤ󡣤ߤƤȡĤ̵ꤷƤȡʾȡˤޤ¿ʬδȤϤΥȤͭꤷȤϤʤΤǤ礦ۥȤˤȤäƤϡ̵ͭϤɤǤ⤤ȤΤ褦ǤȯԤȱļԤ˻ʧ̵ͭˤ餺ƱǤԾϥХ벽ʤǤơ㤤ԾǤˤƤ⡢Υƥϡ좤ƤСع꤬äŻ̤ˤǤ餻ʬҤäƤߤʤΤǡΤʤɮޤʤ줬֤ξQ⤷ޤ󤬡ˡԤ򤳤ܤƤޤޤƼϤ
92ʶ 20:56:14 25731
uchinyan
⡼ޥ󤵤󡢤ʤ¿ѷγΨꡢ򤽤äΤǡͤƤߤޤɤϡƱ褦Ǥ
βˡϡ¿ѷդοǤ뤳ȤȤäơĺ濴 O ĺդȸ뤳ȤȤޤ
餯ŪϡƱȻפޤ
ޤѷΰ A ¿ѷΰĤĺ˸ꤷޤ
ΤȤ B, C ͳ֤Τϡ(2n)C(2) = 2n(2n-1)/2 = n(2n-1)
濴 O ˴ޤϡĤ B, C A 濴 O Ȥκ˰ĤȤ뤳ȤɬפǤ
Ǥϥǡ¦ B 塢¦ C ϡB O Ȥ˴ؤ A ȤȿФ˼ɬפޤ
ϡC ϡAO ˴ؤ B ȿ¦BO ˴ؤ A ȿ¦ΡAO BO Ȥδ֤ˤĺ˸¤뤳Ȥ̣ޤ
äơC ϡAO κ¦ĺ B Τ줾Фơ1, 2, 3, ..., n ̤٤뤳Ȥˤʤꡢ
ɡѷϡ1 + 2 + 3 + ... + n = n(n+1)/2 ̤ꡢˤʤޤ
äơΨϡn(n+1)/2 * 1/n(2n-1) = (n+1)/2(2n-1) Ǥ
βˡ֥ޡȡפɤϡ䡥^^;
ͥνȡ 92ʶ 21:53:24 MAIL:uchi@sco.bekkoame.ne.jp 25733
⡼ޥ
Ϥ褦ޤ
#25730 ʤء
ܤˡ꤬Ȥޤʤ錄ˤϤˤ夤Ƥޤ󤬡

#25733 uchinyan ء
֤ϡC ϡAO ˴ؤ B ȿ¦BO ˴ؤ A ȿ¦ΡAO BO Ȥδ֤ˤĺ˸¤뤳Ȥ̣ޤ
ˡʬ䤹Ǥ

ͧͤȤ̵ֻäơ˥ޡȤʲˡФҲ𤤤ޤ
93ڡ 8:43:32 MAIL:kennji72001@yahoo.co.jp 25734
uchinyan
#25730#25734
ʤήβˡʤС濴ޤޤʤƤ⤤ϡ
x + y + z = 2n-2, 0 <= x, y, z
ꡢ(2n)C(n) ̤ꡣ
濴ޤϡ0 <= x, y, z < n ʤ 0 <= x, y, z <= n-1 ξ郎ղäΤǡ
X = (n-1) - x, Y = (n-1) - y, Z = (n-1) - z Ȥȡ
X + Y + Z = 3(n-1) - (x + y + z) = n-1, 0 <= X, Y, Z
ǡX <= n-1 ʤɤξ¤ɬפǤZ = (n-1) - X - Y >= 0 ꡢX <= (n-1) - Y <= n-1 ƳޤĤޤŪˤפǤ
ǡX + Y + Z = n-1, 0<= X, Y, Z 顢濴ޤ໰ѷϡ(n+1)C(2) ̤ʬޤ
äơΨϡ(n+1)C(2)/(2n)C(2) = n(n+1)/2 * 2/(2n(2n-1)) = (n+1)/2(2n-1) ȤǤޤ͡
ͤȡˡǡ褦ʹͤ򤷤꤬ä褦ʵ⤷ޤ
ͥνȡ 93ڡ 9:54:33 MAIL:uchi@sco.bekkoame.ne.jp 25735
⡼ޥ
#25735 uchinyan ء
ʤۤɡȤʤʬޤ
(1n)k=(n+1)C2 ˤʤǤ͡
94 12:40:12 MAIL:kennji72001@yahoo.co.jp 25736
Ҷ˥ޥ
ʤǡޤƤ֤ȤʤǤ衣ʤ󤫻äΤϵפ֤ǤäѥǻõƤߤ褦Ȼפޤ繥!!(˴طʤȽ񤤤Ƥޤ)
94 18:53:52 25737

ְ㤤̵׻硢ܤ
ᣱߣߡߣȤ롣
ߡʣݣˡᣲߡʡʣݣˡˡ顢
ʣߣߡߣˡߣ¡Ȥʤ롣
ߣߡߣᣴߣᣴߣá
äơᣴߣġȸˤǤ롣
ĤޤꡢФƤСʿˤʤ롣

ȤǡǤ⤹ȻפΤǤ
׻ʿͤɤäʿĴ٤ΤǤ礦

ȡФƣܤۥȤϣޤǤ󤸤ʤʤȤ
դ 95ʷ 9:19:56 25739
աá
(k=1,..,45,47,..,92)k!=
{8743107738480405419313179150952201661905495224577319302239584685312700103754856976135598027629699044959866872510842928691990834347908604982987200404701322398841438365950804030060617008437667585177874676057929995147805052305679632129740277267512339549378486584639597427556608047728739657608495114174341376377251838514779040686304373314552920762393920149534503133347390194628752289447092882327814504116619347168853643841724570872677705282157228310487224870973418361863705771427531582900754386367943044657203613358556246838906936860109373784013124406053954391973017340474008860245376063535299965639317313873222313999758339134073690774736036814019174377647343215459060113791403784429786549291395641771259585581078395458491810937342157206233149823463739204375585527495961690950524542640981418559294364877319512527497682965130954758292077430367602294954960676770249984930319830698199488677781073692047642424550869385366497044532061611762161407770926195964647115345089135109015162158914586774962314923595455156546262740320159498507915998017844551774440807246703042886735682343160403191679793692919769931914034735643122707988480000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}^2
96ʲС 20:07:10 25740
ϥ
ʤĥޤ͡



96ʲС 22:08:08 25741
Ҷ˥ޥ
äͤƱǤϤʤǤ?
97ʿ 19:49:05 25742