ޥ@ݤ
Żΰ߲Ƥޤߥʤ԰¤Ǥġ
Ǥ󤷤㡩 427ڡ 0:22:38 27281
㡼ߡ
޷ŪʲˡϤ褯狼ʤäǡȤꤢֺɸDz򤭤ޤ
ޤ̲ΤǼϤޤ ()
ܹ衡 427ڡ 0:32:27 MAIL:ojamaru@amber.plala.or.jp 27282
ޤ륱
ޤڤäޤäŽäƥ롼ȻȤäơ
󤼤󻻿ʤorz
427ڡ 0:32:54 MAIL:take4310@mobile.email.ne.jp HomePage:ޤ륱27283
CRYING DOLPHIN
ΤڤФǤ͡

ΩΤϡգcmΩΤˤäݤޤ
ΤڤФȤǤѤĺ120٤
̤̤Ȥ뤳ȤˤꡢΤѤΣʬΣ
狼롣äơ6663412cm^3

ΤȤΡĺ120٤ջѷΰ֤Ȥ
cmĹͿ¤˰ϰ(˫)Ǥ͡


http://cdcdcd.sansu.org/pika/junkfoods/q499-3dver-.htm
ǯԥ奦ȡ 427ڡ 0:46:32 HomePage:ȤƻȤ27284
ʤ
գΩΤΣʬΣѤѿΤˣʬΣǤ͡
ߣߣࣳࣴᣱ
427ڡ 0:43:48 27285
Ȥ
Ĥ̤;ȤʿǰʲǤ

褺դοޤa,bȤ
APC;Ѥ
a3:a$
b3:b$
c3:a$
expand(((a3)^2+(c3)^2-(b3)^2)/(2*c3*a3));
b=sqrt(3)*a
ABQ2ʬľѻѷǻʿѤ
a^2+36=b^2
ȭ򤤤
b:sqrt(3)*a$
solve(a^2+36=b^2,a);a=3*sqrt(2)
ȢBCRRC(=a):BC=1:2BC=6*sqrt(2)
դοޤ΢ABCι⤵6
ABC=6^2*sqrt(2)/2=18*sqrt(2)
ȢAPCդACȤ⤵a/2
ȭȤ⤵=a/2=3*sqrt(2)/2
ȭѤǿ1/3ܤ
expand(18*sqrt(2)*(3*sqrt(2)/2)/3);18()
˭ԡ 427ڡ 0:51:04 MAIL:fttnm528@ybb.ne.jp 27286
Ȥ
ȴƤޤ
>expand(((a3)^2+(c3)^2-(b3)^2)/(2*c3*a3));
>b=sqrt(3)*a
2Ĥδ֤
solve(%=-1/2,b)$
part(%,2);
˭ԡ 427ڡ 1:05:03 MAIL:fttnm528@ybb.ne.jp 27287

ǤϤäѤʬ餺Ȥꤢϥ롼ȻȤäƵޤ
θ塢롼Ȥɽ줿դĹͤơäȡΤΣ/ޤ
Ǥ⡢դĹ˥롼ȤĤΤѤ򻻿ǤɤΤʬʤäΤǤ
CRYING DOLPHINʤߤơǼǤ
դcmΩΤ񤭡̤г£á̤οȤУϣˡ
˵ŤʤƤ



427ڡ 10:07:59 27288
LiE
ʤȤޤ򤷤Ǥ
ѿȤȽäƤʤ顢
ѤƤ䡦()
427ڡ 6:29:50 MAIL:njswg145@ybb.ne.jp 27289
⡼ޥ
ä㤤ޤ(^^;)
ʿǹͤƤ⤰㤰ˤʤäƤơ
ֿ޷οޤ򼨤ƤԥȤʤ錄(^^;;)
427ڡ 8:03:26 MAIL:kennji72001@yahoo.co.jp 27290
ޥ
դϼ餤ޤݤߤƬˤ...(^^;;

ϡ㤦ΩΤǤϤޤˤäƤơʪȤƶ褿ΤǤޤǽ餫äƺäƤ褽ʤΤϡ򤯤ۤñʤΤǡˤǤϤޤ

ˤƤC-DϤǤjavaǤꤰžǤޤ餷ʤɤäƺäǤ礦
PowerBook G4 427ڡ 11:57:21 MAIL:masaru-y@sansu.org HomePage:27291
uchinyan
Ϥˤϡ񤷤ä

īȤϡ֤¿ʬ 6cm ΩΤڤФΤʡפȻפƬǤ줳ƤߤƤʬ餺
괺ʿȻѴؿȤä ABC ̤ˤơƬǹ⤵׻ƤߤȤ
ȡ֤ P = Q = R 鲼­P AC ˲­ȡפ뤳Ȥʬꡢ
= 1/3 * (1/2 * (6 * sqrt(2)) * 6) * (6 * sqrt(2))/4 = 36/2 = 18 cm^3
Ȥʤޤǧڤ OK Ǥ

ơŻι֤ˡְ 6cm ΩΤڤФˡͤȤʤͤƤΤǤäʬäƥ˥ޥǤ
ޤ 6cm ΩΤͤĤĺڤȤˡǡդΩΤ̡гˤʤΤڤФޤ
ѤϡΩΤ 1/3 ʤΤǡ6 * 6 * 6 * 1/3 cm^3 Ǥ
θ夬ϫǤۤɤλǤϤʤˡҥȤˤƲȤ (^^;
ǽˡΤȾʬˤޤϲȤʤʬޤ
ˡΤȾʬΡĤäƤ븵ΤդΤۤɤ̤˴ޤޤʤܤΤɤ餫ȡ
վˤϤʤ̤ĤĺȤ̤ʿ̤Ǥ⤦ǤޤƤǤΤΩΤΤ褦Ǥ
ξˡƬǤΤ֤ޤ
ȡǽǤѤȾʬˤʤꡢǤǤäƤ뤳ȤȾʬˤʤޤ
ɡ
= 6 * 6 * 6 * 1/3 * 1/2 * 1/2 = 36/2 = 18 cm^3
ǤʬäƤޤС֤ʤۤɡפʤΤǤʤʤ񤷤

ʤϤ褤赭ǰ٤ 500 Ǥ ^^/
Ȼפä顢轵Ϥ٤ߤ
ˤʤꤽǡ(^^;
ͥνȡ 427ڡ 12:14:01 MAIL:uchi@sco.bekkoame.ne.jp 27292
uchinyan
Ǽɤߤޤϳϫʤ줿褦Ǥ͡ۥäȤޤ (^^;
Ǥ⡥񤭹ߤʤʤ䤷
ȡ

#27284, #27285
ͤȤ⡢ΩΤΤڤФΤϤȤƤ⡢ΩΤΤ 1/4 ȤʬäƤޤȤ
#27284Ȥ­ (^^;
狼롣äơ6663412cm^3
Ǹϡ12 ǤϤʤ 18 Ǥ͡
äˡCRYING DOLPHIN Java ϥʤ
#27291
䤽ˤƤC-DϤǤjavaǤꤰžǤޤ餷ʤɤäƺäǤ礦
ΤˡɤäƺǤ礦
ͥνȡ 427ڡ 12:40:19 MAIL:uchi@sco.bekkoame.ne.jp 27293
ޥ
> ʤϤ褤赭ǰ٤ 500 Ǥ ^^/
> Ȼפä顢轵Ϥ٤ߤ
> ˤʤꤽǡ(^^;

̤ä˿̣Ϥʤơˡ֣ǣפΣϢ٤νפȤǤ٤⸽Ǥʬޤ(^^;;ߥΤʤ褦ˤϤǤ...

ǰȤ櫓Ǥ⣱ǯȤ櫓ǤʤΤǤǣݤ߲ʥղˤǤСȤϻפäƤ⤹ΤǤ̣Τä㤤ޤ
PowerBook G4 427ڡ 13:39:26 MAIL:masaru-y@sansu.org HomePage:27294

ͤΡʿȤä
BCM,ACHȤΩƤơP,Q,BޤPȤޤ
ޤAPAQPCBCaޤ
ѿP-AMCǡPCM60١PCCMa 顢PMa Ǥ
夫鸫ޤͤȡPAPMPCǡAMC90١顢
P ο H 뤳Ȥ狼ޤ
ѡᢤAMCa623a
⤵PH0.5a
äơѿP-AMC3a0.5a30.5a2
Ѥϡ2ܤˤʤ뤫顢a2cm^3ˤʤޤ
ȤơʿȤʤǡa2 ͤޤʤȹͤΤǤͤˤ̵Ǥ
ɡʿѤƵ᤿ aͤ򣲾褷ơ18cm^3 ȵޤ
427ڡ 14:46:23 27295
CRYING DOLPHIN
#27291 etc
ưĿޡϻäƴñäꤷޤ
٤եȶֺɸμïǤޤ

ˣĿɽɬפʣĤΥե(Graphics3D.classʤ)
ŸޤȤΩƤƸޤĺζֺɸİ
٤ˡǤäƶֺɸhtmlե˹߹

ä
֥åꤷƤǤ㤦(^^;

Ŀޤɽ٤ɬפʥեɤGETǤΤ
ϤʤꤷΤǡɤꤷ˺ޤ
ǯԥ奦ȡ 428ʶ 0:34:35 HomePage:ȤƻȤ27296
ڼ
#27294
夲Ǥ礦
ϢͽϷޤäƤʤΤǡ֤Хղ⤤Ǥ͡
͡ 428ʶ 5:17:01 MAIL:iida@ae.keio.ac.jp 27297
⡼ޥ
CD3D򥰥ꥰꤷơưˤäǤޤ(^^;)
οޤƬ˥᡼Τϡ錄ˤ̵(^^;;)
ǤΤκƱΤεΥΥ᡼Ǥޤ(OrZ)
428ʶ 7:53:50 MAIL:kennji72001@yahoo.co.jp 27298
ϥ饮㡼ƥ
褦ʿͤˤϤޤ󤬡
ؤζʿͤϤ˸ޤ

Ĵ٤ΤѤ˥إθޤ
ñդĹϽФΤǸޤ

̶彣 429ڡ 14:17:52 HomePage:ĩ27299
ޥ
#27297
Ϣ桢㤢ޤ󤬡5/2ϤɤʡȤפäƤޤޤ硹Ū罸ϤʤΤǡޤȤˤʤȻפޤ
PowerBook G4 428ʶ 22:06:15 MAIL:masaru-y@sansu.org HomePage:27300
ҡΤ
٥ȥǤꤴޤʡ
9ߤ濴 429ڡ 0:19:19 HomePage:27301
⡼ޥ
4320000äƽФޤ
ǤȤޤ
4444444ܤï͡
429ڡ 20:25:31 MAIL:kennji72001@yahoo.co.jp 27304
ݤ
ղǼ򤫡
ǤƤ͡
ƤӤʤޤ餷ޤ
ǤԤäƤ
Ƹɡ 430 11:26:18 MAIL:hopes@mba.ocn.ne.jp HomePage:ȣϣУţӤ褤Ȥ٤Ϥ27305
Ȥ
#27299
>Ĵ٤ΤѤ˥إθޤ

λǤʲ򥫥ޤ
ǤϥĢǥԥڰȯ
xmaxima(FREE)ǰʲǤ

a:6*sqrt(2)$
b:3*sqrt(6)$
c:3*sqrt(6)$
d:3*sqrt(2)$
e:3*sqrt(6)$
f:3*sqrt(2)$
expand((a^2*b^2*d^2+b^2*c^2*e^2+c^2*a^2*f^2+b^2*a^2*e^2+c^2*b^2*f^2+a^2*c^2*d^2
+c^2*e^2*f^2+a^2*f^2*d^2+b^2*d^2*e^2+c^2*d^2*f^2+a^2*e^2*d^2+b^2*f^2*e^2)
-(a^2*b^2*c^2+a^2*e^2*f^2+b^2*f^2*d^2+c^2*d^2*e^2)
-(a^4*d^2+a^2*d^4+b^4*e^2+b^2*e^4+c^4*f^2+c^2*f^4))$
sqrt(%)/12;18()

ȿȤƤϾѤοˤ϶̣ޤ
freeΤΤФ(15ƥर餤ǶfreeǤʤʤämupadȤ )ǾѤmathematicaȤmapleȤˤƤޤ
˭ԡ 430 13:59:21 MAIL:fttnm528@ybb.ne.jp 27306
⡼ޥ
ʵʬž˹ͤƤߤƲ(^^)

˲ʸΡˤϲǤ礦

B A C B D C E D F ?

˲οΡˤϲǤ礦ͭ̾䡩

0101110311013211013123110?
430 23:07:03 MAIL:kennji72001@yahoo.co.jp 27307
weapon
1 E
2 23124110
51ʷ 1:16:14 27308
⡼ޥ
#27308
weapon󡢤
ʤߤˣˤ Mensa IQ test ˺ܤäƤޤ
51ʷ 8:41:44 MAIL:kennji72001@yahoo.co.jp 27309
uchinyan
#27307, #27308, #27309
⡼ޥ󤵤weaponء
1) ʬޤ٤ߥܥʤΤ2) 򸫤ƤͳʬʤǤ (^^;
ɤơ
2 23124110
ˤʤΤǤ
ͥνȡ 51ʷ 8:56:53 MAIL:uchi@sco.bekkoame.ne.jp 27310
⡼ޥ
#27312
uchinyanء
0ο1οɽƤǤ
äƥץǤ硪ʰƳʡ
51ʷ 10:08:19 MAIL:kennji72001@yahoo.co.jp 27311
粬ҹ
ƬȤΩƤƲȤǤޤʡ
ϤҤ᤭ʤǡ겡ѤʤȤˤʤꤽǤ͡
51ʷ 11:36:31 MAIL:toshi009@land.hokuriku.ne.jp 27313
uchinyan
#27311
ϡ󡢤Ȥ
0ο1οɽƤǤ
οΡǤ͡
0 : ˤϲʤ顢괺 0 ʡ
10 : 0 ʤΤǡ0 1 ġ
1110 : 10 ʤΤǡ1 1 ġ0 1 ġ
3110 : 1110 ʤΤǡ1 3 ġ0 1 ġ
132110 : 3110 ʤΤǡ3 1 ġ1 2 ġ0 1 ġ
13123110 : 132110 ʤΤǡ3 1 ġ2 1 ġ1 3 ġ0 1 ġ
äơ
23124110 : 13123110 ʤΤǡ3 2 ġ2 1 ġ1 4 ġ0 1 ġ
ȤȤϡθϡ
1413223110 : 23124110 ʤΤǡ4 1 ġ3 1 ġ2 2 ġ1 3 ġ0 1 ġ
1423224110 : 1413223110 ʤΤǡ4 1 ġ3 2 ġ2 2 ġ1 4 ġ0 1 ġ
2413323110 : 1423224110 ʤΤǡ4 2 ġ3 1 ġ2 3 ġ1 3 ġ0 1 ġ
1433223110 : 2413323110 ʤΤǡ4 1 ġ3 3 ġ2 2 ġ1 3 ġ0 1 ġ
1433223110 : 1433223110 ʤΤǡ4 1 ġ3 3 ġ2 2 ġ1 3 ġ0 1 ġ

(ʲѡ)

Ȥ櫓Ǥ͡
ࡢǸΤȤǡ1433223110 ȤĤͤ˼«ƤޤΤϰʳǤ

äɲá
ʤߤˡο󥵥Ȥõ顢id:A036058
http://www.research.att.com/~njas/sequences/A036058
ǤޤˤΥȤˤϡޤ͡
ͥνȡ 51ʷ 12:44:21 MAIL:uchi@sco.bekkoame.ne.jp 27314
⡼ޥ
#27314
uchinyanء
ء«ä³ΤȤФפäƤޤ(^^;
51ʷ 13:37:32 MAIL:kennji72001@yahoo.co.jp 27315
uchinyan
#27315
⡼ޥ󤵤󡢸ꡢ
䣲˲οΡˤϲǤ礦ͭ̾䡩
0101110311013211013123110?
դȡѤʤȤפĤޤ12234110 Ǥ⤤ΤǤϤʤΤʤäơ

ǽ23124110ϡο˽иƷο򡢽иν֤˴طʤ
a3b2c1d0 η0 ĤξϽ񤫤ʤȤơθĿ񤤤Ƥޤ͡
򡢤äȤҤͤƤޤο򱦤鸫ƹԤäƳƷοи֤εսˡ
a3b2c1d0 ηΡa3, b2, c1, d0 ¤Ѥ롢ȤǤǤ
Ĥޤꡢ
0 : ˤϲʤ顢괺 0
10 : 0 ʤΤǡ鸫ƹԤäơ0 1 Ĥǡνи0 εս 0 ν 10 ¤٤ơ10
1110 : 10 ʤΤǡ鸫ƹԤäơ0 1 ġ1 1 Ĥǡνи0, 1 εս 1, 0 ν 11, 10 ¤٤ơ1110
3110 : 1110 ʤΤǡ鸫ƹԤäơ0 1 ġ1 3 Ĥǡνи0, 1 εս 1, 0 ν 31, 10 ¤٤ơ3110
132110 : 3110 ʤΤǡ鸫ƹԤäơ0 1 ġ1 2 ġ3 1 Ĥǡ
νи0, 1, 3 εս 3, 1, 0 νˡ13, 21, 10 ¤٤ơ132110
13123110 : 132110 ʤΤǡ鸫ƹԤäơ0 1 ġ1 3 ġ2 1 ġ3 1 Ĥǡ
νи0, 1, 2, 3 εս 3, 2, 1, 0 νˡ13, 12, 31, 10 ¤٤ơ13123110
ȤʤäơβǤ̷⤷ޤ
ȡϡ
12234110 : 13123110 ʤΤǡ鸫ƹԤäơ0 1 ġ1 4 ġ3 2 ġ2 1 Ĥǡ
νи0, 1, 3, 2 εս 2, 3, 1, 0 νˡ12, 23, 41, 10 ¤٤ơ12234110
Ȥʤޤ

ǤѤʤȤפäȤȡץ񤤤Ƥߤ褦ʡȻפäƥ르ꥺͤƤȤˡ
֤ʤäǤ
ʤβǸ¤ؤפˤʤΤǡץϼ㴳ڤˤʤꡢβϼˤϤǤʤȻפޤ

ʤߤˡξˤ⡢
12234110 -> (0,1), (1,3), (4,1), (3,1), (2,2) -> 10, 31, 14, 13, 22 -> 22, 13, 14, 31, 10 -> 2213143110
2213143110 -> (0,1), (1,4), (3,2), (4,1), (2,2) -> 10, 41, 23, 14, 22 -> 22, 14, 23, 41, 10 -> 2214234110
2214234110 -> (0,1), (1,3), (4,2), (3,1), (2,3) -> 10, 31, 24, 13, 32 -> 32, 13, 24, 31, 10 -> 3213243110
3213243110 -> (0,1), (1,3), (3,3), (4,1), (2,2) -> 10, 31, 33, 14, 22 -> 22, 14, 33, 31, 10 -> 2214333110
2214333110 -> (0,1), (1,3), (3,3), (4,1), (2,2) -> 10, 31, 33, 14, 22 -> 22, 14, 33, 31, 10 -> 2214333110
ȤʤäơϤ«褦Ǥ
Ի׵ġ

ο󥵥ȤˤϡβοϤʤ褦Ǥ
ͥνȡ 51ʷ 15:31:21 MAIL:uchi@sco.bekkoame.ne.jp 27316
⡼ޥ
#27316
uchinyanء
ʤۤɡ褯פĤޤ͡
logical餤Ȼפʡ(^^)
̣̤ϰĤǤʤƤ⤤Ǥ͡
顢13123110 ,23124110,? ˤФ褫äǤ͡

ĤǤιͤС

1,2,4,6,10,12,?

ϴñʡ(Ȼפä顢줤ο󥵥Ȥ˺ܤäƤ(^^;

ʤ餳ϡʤΥȤˤܤäƤʤ(^^)

2,0,3,0,4,8,1,?

51ʷ 16:30:25 MAIL:kennji72001@yahoo.co.jp 27317
uchinyan
#27317
1,2,4,6,10,12,?
ϡˤʬޤǿǤ͡ǡ17 - 1 = 16 Ǥ礦
2,0,3,0,4,8,1,?
äϡࡥ
ͥνȡ 51ʷ 21:15:54 MAIL:uchi@sco.bekkoame.ne.jp 27318
⡼ޥ
#27318
uchinyanء

2,0,3,0,4,8,1,?
äפĤοǤ(^^)
ϤꤢѴ򤹤ȻѤƤޤ
51ʷ 22:31:09 MAIL:kennji72001@yahoo.co.jp 27319
ʤ
#27319
2,0,3,0,4,8,1,?

³ϡ5,4,2,4 ʡ
mobile 52ʲС 1:25:49 MAIL:naka@sansu.org HomePage:ʤ27320
ERĹ
ʤ⤯ơޤλDz򤤤Ƥߤޤ(^^;
http://www.geocities.jp/taki_math/kaihou499.html

52ʲС 1:34:34 27321
sugitakukun
#27319
>2,0,3,0,4,8,1,?

Ф餯Ǻߤޤˤ⸫ޤ
ؤ⹻ζʽǡѴפǺܤäƤޤ
ܣ˻ԣӶ衡 52ʲС 3:41:26 MAIL:sugitakuunikun@msn.com HomePage:White Shadow27322
⡼ޥ
#27320
ʤ
sugitakukunⵤŤ줿褦Ǥ͡(^^)
52ʲС 9:53:17 MAIL:kennji72001@yahoo.co.jp 27323
uchinyan
#27319
2,0,3,0,4,8,1,?
äʬޤ߼ΨγƷ塼Ǥ͡
äϡʤƱ
³ϡ5,4,2,4 ʡ
Ǥ礦
¤ϰƬ򤫤᤿ΤǤƬǤϡ = 3.1416... ˤʤäƤơ֣ܤʤʡפȻפäƤޤ𤱤ʤ
3.1416 ϶ͤǡϡ = 3.1415926535... ʤΤǡפޤ͡
򴪰㤤ƤȤ˵դƲạ̈Ǥ⡢ ^^/
ͥνȡ 52ʲС 10:41:04 MAIL:uchi@sco.bekkoame.ne.jp 27324
uchinyan
ǽƥȤΤ褦꤬³Τǡ֤ˡäݤġ
ˤʤ顢ͤƤߤƤ


ɽοܤ4ܤ610ޤ
ê˰¤٤뤳Ȥͤޤ
(1) ܤɽοʳǶ̤ʤȤȡܤ٤ʤ¤ϲ̤ꤢޤ
(2) (1)ξγΤ餷ΨƤ
(3) ٤Ƥܤ̤Ȥơ(1) ڤ (2) ͤƤߤƤ

ϡɤä褦ʵޤͶƳˤơäݤפޤ
ηǼĤäۤɤοͤʤСñʡ
ͥνȡ 52ʲС 10:59:24 MAIL:uchi@sco.bekkoame.ne.jp 27325
⡼ޥ
#27324
uchinyanء
̤
Ǥ褽ΥȤΡ롼Ȥʼ¤Ϣ3ˤμäƤŹɤäȤޤ⤦˺㤤ޤɤ͡(^^;)
52ʲС 11:04:12 MAIL:kennji72001@yahoo.co.jp 27326
⡼ޥ
#27325

ɽοܤ4ܤ610ޤ
ê˰¤٤뤳Ȥͤޤ
(1) ܤɽοʳǶ̤ʤȤȡܤ٤ʤ¤ϲ̤ꤢޤ
(2) (1)ξγΤ餷ΨƤ
(3) ٤Ƥܤ̤Ȥơ(1) ڤ (2) ͤƤߤƤ

(1) 6ΤȤʤˤФ褤Τǡ7C4=35 ̤ꡣ
(2)٤Ƥ¤ϡ10!/4!6!=210 ʤΤǡ(1) ˤʤΨϡ35/210=1/6
(3)٤Ƥ̤ʤ顢(1)ϡ35*4!*6! ̤ꡣ (2) ϡʬʬҤ 4!6! Ǥä뤫顢Ʊ 1/6

ñ褦ʵ
52ʲС 11:17:41 MAIL:kennji72001@yahoo.co.jp 27327
uchinyan
#27327
ϡ˴ñޤǤ
ĿŪ򤤤ʡȻפäΤϡ(2) (3) γΨפǤ
ͥνȡ 52ʲС 11:27:11 MAIL:uchi@sco.bekkoame.ne.jp 27328
uchinyan
ϡ줬٤ߤʤΤǡȤäƤϲǤꡢɤǤ礦
ˤʤ顢ͤƤߤƤ (^^;
ȤؼϢηǼĤǸΤǤʬäݤʤʤ򤤤Ȼפޤ
⡢ˤϴñʡ


ε§ǿĤ˽񤤤ƤȤͤޤ
§Ĥ˿ȥ񤤤ƤȤȥµڤѤᡢ­񤯤ȤǤ롣ʤȥƱǤ褤
ǽˡĤ˿ 1 2 񤫤ƤȤޤǡ㤨С
(1 + 2) + 1 * 2 = 5, (1 + 1) + 1 * 1 = 3
ʤɤο­ȤǤޤθϡ5 3 Ȥޤ
ξǡοĤ˽񤯤ȤǤޤ
(1) 13121
(2) 12131
(3) 21311
(4) 31211
;͵С񤱤ʤää硢ǽͿɤФͤƤߤƤ
ͥνȡ 56ڡ 12:15:01 MAIL:uchi@sco.bekkoame.ne.jp 27329
⡼ޥ
#27329ʹĤο
򤽤ʤΤǹͤƤߤޤ

ϡ1,2,3,5,7,8,11,15,17,23,26,31,35,
a*b+a+b=a*b+a+b+1-1=(a+1)(b+1)-1=m
(a+1)(b+1)=m+1
Ĥޤꡢ(a+1) m+1 ʤ櫓顢
m+1 ΰ˸ܣˤʤʤȤᡣ
13122=2*3^5*17ϡ2-1=1,3-1=2 Ϥ뤬17-1=16ϤʤΤ̵
121312=2*4^2*17*223 ǤϤ̵
21312=3^2*4^3*37 ǡ37-1=36 ϤʤΤ̵
31212=3^3*4*17^2 ǤϤ̵

ǽɬפʿϡ㤨С13122=2*3^5*17 ʤΤǡ
3=(0+1)(2+1) ǡ0,2 ɬס
2=(0+1)(1+1)ǡ0,1 ɬס
17=(0+1)(16+1) ǡ0,16 ɬס
ʲƱͤ˹ͤФΤʡ

57 5:02:32 MAIL:kennji72001@yahoo.co.jp 27330
uchinyan
#27330, #27329
ͤOKǤ׻ߥ褦Ǥϡ
(1) 񤱤롣(2) 񤱤ʤ(3) 񤱤ʤ(4) 񤱤ʤ
ˤʤޤ

ݥȤϡ⡼ޥ󤵤ΤŦɤꡢȥȤ򥦤Ȥȡ
ܣ(ܣ)(ܣ)
ˤʤ뤳ȤǤϡĤ˽񤫤Ƥ뤹٤ƤοФƤޤ
ǡܣ ʤɤʬǤơɡǽͿƤ롢1 + 1 = 2 2 + 1 = 3 ޤǤɤ夭ޤǸĤϡʬǤޤ
դθ򤹤ȡĤ˽񤱤 +1 ϡɬ2 3 ǰˤʤȤȤˤʤޤ
äơ+1 ǰʬ򤷤Ƥߤơ
(1) 13121 + 1 = 13122 = 2^1 * 3^8 ǡ񤱤롣
(2) 12131 + 1 = 12132 = 2^2 * 3^2 * 337 ǡ񤱤ʤ
(3) 21311 + 1 = 21312 = 2^6 * 3^2 * 37 ǡ񤱤ʤ
(4) 31211 + 1 = 31212 = 2^2 * 3^3 * 17^2 ǡ񤱤ʤ
Ȥʤޤ

̤ˡǿ p ФƤϡp = p * 1 ǽǤʤΤǡ+1 ηѷ褦ȤƤ⡢
(p-1) + 1 = p = p * 1 = ((p-1) + 1) * (a + 1)
Ȥʤ褦 a ϡǽͿƤ 1, 2 ǤϹǤޤ
äơ+1 ǰʬ򤷤Ȥ 2, 3 ʳǿˤϹĤˤϽ񤱤ޤ
񤱤褦ˤˤϡǿ p Ф p-1 ǽͿƤɬפޤǡ
(2) 337 - 1 = 336 򡢺ǽͿɲä롣
(3) 37 - 1 = 36 򡢺ǽͿɲä롣
(4) 17 - 1 = 16 򡢺ǽͿɲä롣
Ȥʤޤ
ʤ0 ϡ٤Ƥο a Фơ
0 * a + 0 + a = a
ѤʤΤǡɲäƤ⤤ǤѾ̣Ϥޤ

ȤƤϡ㤨С
ͤϰϤȤơε§ 1 100 ޤǤΤ٤Ƥο褦ˤˤϡ
ʤȤǽˤĤΰۤʤͿɬפޤ
ȤˤƤߤƤ⤤Ǥ礦͡
ϡäդɬפǤޤ⤦ˤʬǤ礦顢ƽ񤫤ʤǤޤ礦 (^^;

ʤܼϡf(x) = x+1 ѴǡͿ줿§ǹ뽸ȡ̾γݤǹ뽸Ȥ
Ʊ¤ĤȤˤ뤽ǤϡȾʬϡǤ餺 (^^;
Τ褦äǤ빽Ͽإ٥ؤʤɤǤδŪʳǰǤ롢
Ĥν礬黻˴ؤƱ¤ĤȤƱ(ϡֽƱסf Ͱ˰¸ޤ)Ȥǰ
ȴطƤ褦Ǥ
ˡ§α黻 @ Ȥ a @ b = a * b + a + b 顢f(a @ b) = f(a) * f(b)
ݤ * ηˡ§ˡ§ñ̸¸ߤʤɤ @ бǤ뤳ȡ
ˡ̾­ + Фơa # b = a + b + 1 ƳȡƱͤΤȤʬˡ§⤤뤳ȡ
ʤɤʬȻפޤ
äơ餫鹽νϡα黻˴ؤƱĤȤˤʤޤ
ϡǿǰʬʤɤòΤȹͤޤ
ͥνȡ 57 13:01:40 MAIL:uchi@sco.bekkoame.ne.jp 27331
⡼ޥ
#27331
>ͤϰϤȤơε§ 1 100 ޤǤΤ٤Ƥο褦ˤˤϡ
ʤȤǽˤĤΰۤʤͿɬפޤ


2101ޤǤǿοɬס
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101 26ġ
ºݤ˹ľˤϡ餫1

13122=2*3^8 Ǥ͡褯ְ㤦Ǥ(^^;
Ǥ(^^)

57 14:29:31 MAIL:kennji72001@yahoo.co.jp 27332
⡼ޥ
פĤǤ

n!=m!(m-1)! ΤͤƤޤ(n,m)=(1,1),(2,2),(10,7) ʳ¸ߤΤǤ礦
ѷơm*n!=(m!)^2 ˤϤʤǤ
˻פΤǤ
ɤäƾФΤʤ
57 16:32:22 MAIL:kennji72001@yahoo.co.jp 27333
sugitakukun
#27333
פĤˤϻפĤβʤ

n!=m!(m-1)!n!/m!=(m-1)!ѷ

n*(n-1)**(m+1)=(m-1)!

ǡֱդικǿܤդ˴ޤޤʤФʤʤפΤȡֺդιǿäƤϤʤʤפȤ顢դικǿ֤Ȥ¡㣲ǿ¤ϡĤޤǡʣǿǤ褤ˤ¸ߤǤʤ
Τ褦ǿ7ʾ¸ߤʤȤоλΤϤʤǤ

Ȥϡξդǰ˴ޤޤ룲θĿn!ΰοϣ˶Ťˤ顢ξդι礭ʺФƤϤʤΤȤξդͤˤ礭ʺǤ롢äƤˡͤޤ

ǸޤǵͤʤäΤǡΤͶƤ^^;
ܣ˻ԣӶ衡 57 19:30:53 MAIL:sugitakuunikun@msn.com HomePage:White Shadow27334
⡼ޥ
#27334
sugitakukunءͤƲäơ꤬Ȥޤ(OrZ)

ֱդικǿܤդ˴ޤޤʤФʤʤפΤȡֺդιǿäƤϤʤʤפȤ顢դικǿ֤Ȥ¡㣲ǿ¤ϡĤޤǡʣǿǤ褤ˤ¸ߤǤʤ

줤Ǥ͡ʤ錄⤽ʴʥХȡˤǡ10ʾˤʤä顢ǿƤ뤫顢դǤϥСʤʤʡäƹͤƤޤ
2<3<4
3<5<6
5<7<10
7<11,13<14
顢ΩȤ顢m-1<7 Ĥޤꡢ1m7 ޤǤˤʤ
ˡ7礭ǿ p Ǥϡp<q<2q ǿ2İʾ夢äƸʤƤϤʤʤ
̤οǡ2 ǿϺ1ĤϤ뤳ȤϾƤޤʥӥդˤȤäƲʤΤʡ
⤦äȹͤƤߤޤ(^^)

ɲá
m*n!=(m!)^2顢m 7 ʲʤ顢 n 10 ʲʤξդοǿμƱ
n 11 ʾʤ顢m 11 ǰ˻ʤȥǡλϡn ϺǤ 11+1=12 ʾˤʤ뤬դκǿ11 ʲ 7 Ϻդ2ʤȥǡĤޤꡢn ϺǤ 2*7 ʾˤʤ롣
11<13<14 ʤΤǡդˤϡ13 οǰɬפȤʤꡢm 13 Ȥȡn դ ǿ 13 ʲ 11 2ʤȥǡĤޤꡢn ϺǤ⡡2*11 ʾˤʤ롣
13<17,19,<22 ʤΤǡդˤϡ17,19 οǿ졢m 19 Ȥȡդˤ 17 2󤢤Τǡn 2*19 ʾȤʤꡢϤꡢ19<23,29,31,37<38 ȺǤ⿷ǿӥդ1Ĥϸ뤿ᡢϱʱ³Τ̵
ǾˤʤäƤޤͤ
58ʷ 7:44:50 MAIL:kennji72001@yahoo.co.jp 27335
uchinyan
#27335
⥢ץ㤦ΤǤ褦ʤȤͤƤޤ
n! = m! * (m-1)! ξդ m 򤫤 m * n! = m! * m! ˤơ
ХȤǤn! n/2 n ˥ӥդȤȡn/2 < p < n ʤǿ p ¸ߤޤ
̩ˤϡn ǾʬɬפǤ礦
n < 2p ʤΤǡp n! ˰󤷤ޤ󡣱դʿʤΤǡm = p ǤʤȡΩޤ
ǡm Ϥǿ p ˷ꤷ
p * n! = p! * p!
n! = p! * (p-1)!
n * (n-1) * ... * (p+2) * (p+1) = (p-1)! = (p-1) * (p-2) * ... * 3 * 2 * 1
ơɤΤȻפäƤޤ
n/2 n ˤ⤦ǿ q С p ȹ碌ĤǤۤ͡ɤƱͳDz¸ߤޤ
äơn Ͱʾǿİʾ夢뤳ȤǤʤʡȤȤȡ
դ p 꾮ǿ٤ n/2 ʲΤȤˤ˾ʤʤʡȻפäƤޤ
ԤιͤΤͤƱǤ͡ʴ⤹ΤǤ
ӥդξΤʤΤǤξʬСɤȤǤʤΤǤ礦
ͥνȡ 58ʷ 7:50:36 MAIL:uchi@sco.bekkoame.ne.jp 27336
uchinyan
#27335ɲʬ
ʤۤɡʤʤ򤽤Ǥ͡ޤԤʵޤ⤦ä긡ƤƤߤޤ
ͥνȡ 58ʷ 8:01:40 MAIL:uchi@sco.bekkoame.ne.jp 27337
⡼ޥ
#27335
>ɲá
m*n!=(m!)^2顢m 7 ʲʤ顢 n 10 ʲʤξդοǿμƱ
n 11 ʾʤ顢m 11 ǰ˻ʤȥǡλϡn ϺǤ 11+1=12 ʾˤʤ뤬դκǿ11 ʲ 7 Ϻդ2ʤȥǡĤޤꡢn ϺǤ 2*7 ʾˤʤ롣
11<13<14 ʤΤǡդˤϡ13 οǰɬפȤʤꡢm 13 Ȥȡn դ ǿ 13 ʲ 11 2ʤȥǡĤޤꡢn ϺǤ⡡2*11 ʾˤʤ롣
13<17,19,<22 ʤΤǡդˤϡ17,19 οǿ졢m 19 Ȥȡդˤ 17 2󤢤Τǡn 2*19 ʾȤʤꡢϤꡢ19<23,29,31,37<38 ȺǤ⿷ǿӥդ1Ĥϸ뤿ᡢϱʱ³Τ̵

ְ㤤ޤ
n ϡ2*17 ʾȤʤꡢ19<23,29,31<34 ޤǤޤ͡
餳ΤޤޤǤϡӥդȤʤ(^^;
ǿp_k ȡǿ p_(k-1) ǿǡ
p_k<q<2p_(k-1) ǿ q 1Ĥ뤳ȤФΤǤ
¿ʬñǤϤʤ͡(^^)

Ʊp_k<p_(k+1),p_(k+2)<2p_k ȡ˾ʤȤ2Ĥǿ¸ߤƤ⤤Ȼפޤ
58ʷ 11:16:56 MAIL:kennji72001@yahoo.co.jp 27338
uchinyan
#27338
p_k<q<2p_(k-1) ǿ q 1Ĥ뤳ȤФΤǤ
Ǥ͡ƸƤƤߤơƱˤʤޤ

ȤǡĤۤɼ䡣
1ӥդϡɤäƾΤǤ
2λפդפդäˤʤΤǤ
ͥνȡ 58ʷ 11:15:50 MAIL:uchi@sco.bekkoam.ne.jp 27339
uchinyan
#27338¾
⡼ޥ󤵤ء
ڥǥWikipediaˤǡõƤ顢ιܤ򸫤Ĥޤ

٥ȥβ
ŵ: ե꡼ɴʻŵإڥǥWikipediaˡ

٥ȥβȤϡ1845ǯ˥ե󥹤οؼԥ٥ȥȯɽؾͽۡ
1850ǯ˥ӥդΤǡºݤǤ롣Τ(˱˥ӥդȤƤ֡

ʲ꤬̿Ǥ롣

n3礭ǤС n < p < 2n-2 ʤǿp¸ߤ롣

ˡݡ롦ǥϰʲChoquet theory)

6礭nФ n < p < 2n ʤǿpϾʤȤ2¸ߤ롣,2ĤΤĤ4k+1 ηǤ ¾ 4k+3 ηǤ롣

ʤȡݡ롦ǥˤĥȤС
6礭nФ n < p < 2n ʤǿpϾʤȤ2¸ߤ
ȤΤǡ򿮤СפդϡƤ褦Ǥ
äȤ⡢ξϤɤ
ͥνȡ 58ʷ 11:37:30 MAIL:uchi@sco.bekkoam.ne.jp 27340
⡼ޥ
#27339
uchinyanء
¤ϡKaito ΥȤ98280 η׻פĤޤ
ӥդñˡʤȸäƤ錄ɤǤ褯狼ʤä˥ǥ夵󤬾ƤޤΥɤ⤤ޤϤʤǤ(^^;
鸫Ĥ뤫͡

ɲäǽ񤭤ޤƱ̣ǡp_k<p_(k+1)<p_(k+2)<2p_k
ǿ2İʾ夢뤳ȤƤ⤤Ȼפޤ

ˤƤȤǤʤȾ̵ʡ

õƤʲΤ褦ʽ񤭹ߥȤ򸫤Ĥޤ
ʿ

褬ʿˤʤʤȤξ򲿿ͤĺޤɤβԤӥդʣȣδ֤ˤɬǿˤȤäƤޤɤŪˤϽʤΤǤ礦Ʊͤǣ෸ʿˤʤ뤫Ȥͤޤˤϥǥθʲ餷ʿˤϤʤʤȻפޤŪʾǤ礦2003/1/19
http://www.edu.gunma-u.ac.jp/~seyama/sol.html
58ʷ 13:32:57 MAIL:kennji72001@yahoo.co.jp 27341
⡼ޥ
#27340
uchinyanءOrZ

>ʤȡݡ롦ǥˤĥȤС
6礭nФ n < p < 2n ʤǿpϾʤȤ2¸ߤ ȤΤǡ򿮤СפդϡƤ褦Ǥ

ˡǸޤ͡
ʤäꤷޤ(^^)

Ǥ⡢ǥ夵Ϥɤäƾ줿Ǥ礦ͤ
ʬꤿǤͤ
58ʷ 13:43:42 MAIL:kennji72001@yahoo.co.jp 27342
uchinyan
#27341, #27342
ӥդΥǥ夵ξPDF򸫤Ĥޤ
http://www.cmo.jp/users/tapooh/academic/archives/chebyshev.pdf
or
http://www1.ocn.ne.jp/~yoshiiz/pdf/chebyshev.pdf
äɤǤϡƤƱǤ㴳Ƽιפ褦ǤäɤǤߤޤ
ǥ夵ˤĥ
6礭nФ n < p < 2n ʤǿpϾʤȤ2¸ߤ
ϡޤĤޤ (^^;
ɲäǽ񤭤ޤƱ̣ǡp_k<p_(k+1)<p_(k+2)<2p_k
Ϥϡǥ夵γĥ餫Ǥ͡
ޤp_k n ʲκǿȤȡ n < p_(k+1) ڤ 2 * p_k <= 2n ʤΤǡp_(k+1)<p_(k+2)<2p_k С
ǥ夵γĥǿη 4k+1, 4k+3 ȤΤϽ⤤ޤ͡
ʤ
並漼http://www.edu.gunma-u.ac.jp/~seyama/sol.html
ʤʤ򤽤ʤȤ񤤤Ƥ褦Ǥ
ͥνȡ 58ʷ 15:19:17 MAIL:uchi@sco.bekkoam.ne.jp 27343
⡼ޥ
#27343
uchinyanء
򸫤ĤƲꤢ꤬Ȥޤ
ɤǤʬ뤫ɤʬޤ󤬡錄ޤɤǤߤ褦顣(^^;)
OrZ
58ʷ 15:38:44 MAIL:kennji72001@yahoo.co.jp 27344
uchinyan
#27343
ӥդΥǥ夵ξPDF򸫤Ĥޤ
http://www.cmo.jp/users/tapooh/academic/archives/chebyshev.pdf
or
http://www1.ocn.ne.jp/~yoshiiz/pdf/chebyshev.pdf
ɤڡΤΤǤΤǡ̤ꡢɤǤߤޤܸǤ ^^;
ӥդΥǥ夵ξϤˤƤ褦ǤñʤҲǤϤʤơ
ϳԤľܤ˻ͤˤαƶơ󡢴ܤƱǤ̯˹פƤ褦Ǥ
ΥݥȤϡɤ⡢
n < p < 2n ʤǿ p ¸ߤʤȲꤷơ෸ C(2n,n) = (2n)!/n!n! ɾȡ̷⤬Ƴ롣
ȤñʤΤǤȤäƤƻ⡢ñʤʸη׻ɾ餤ǡŪǤ
餯줬ǥ夵ξܼʤΤǤ礦
ñȤäơΤñʬ䤹Ȥɬ⤽ǤϤʤ
̷Ƴ C(2n,n) ɾ񤷤Ǥ
礦ɡإԥåΤ褦ʴǤ礦
إԥå򥹥饹򤱤ͤʤСȼ˹ͤդȤǽȻפޤ
ʤĤξƱȤ򤷤ƤΤǤŪʼͿʤɤ̯˰㤦Τǡ٤Ƥߤȡ򤬿ʤȻפޤ
ºݤξܺ٤ϡѻǤɤǤ餦ȻפΤǾάޤ

ʤ
䤿ǥ夵ˤĥ
6礭nФ n < p < 2n ʤǿpϾʤȤ2¸ߤ
ϡޤĤޤ (^^;
ϡɡ饤ǤϸĤޤǤhttp://mathworld.wolfram.com/ChoquetTheory.html ˡ

Choquet Theory
(ΤǤ礦)
...
Erdos proved that there exist at least one prime of the form 4k+1 and
at least one prime of the form 4k+3 between n and 2n for all n > 6.
ǥϡn > 6 Ȥʤ뤹٤Ƥ n Фơn 2n Ȥδ֤ˡ
4k+1 ڤ 4k+3 ǿʤȤĤġ¸ߤ뤳Ȥ
...
REFERENCES:
ʸ
Erdos, P. "A Theorem of Sylvester and Schur." J. London Math. Soc. 9, 282-288, 1934.

Ȥޤ

⡼ޥ󤵤λפĤ򤯤ˤϡn >= 6 n 2n Ȥδ֤ǿʤȤ¸ߤ뤳ȤǽʬǤ
ʤСۤɤΡӥդΥǥ夵ξäȲɤСñ˾Ǥ褦Ǥ

ǤϡϤȤ (^^;Ǥ礦
ͥνȡ 59ʲС 11:51:03 MAIL:uchi@sco.bekkoame.ne.jp 27345
⡼ޥ
#27345
uchinyanء
⤢꤬Ȥޤ
PDFɤǤĤƹԤޤ(^^;
m*n!=m!(m-1)! ϡǤǤǤ(^^)

<õ>
錄ϤĤ֥ɥХåϤפƬ⤫Ǥޤ
16ʾζ2Ĥǿɽ蘆äƸʤʤ

6ʾnʤ顢6<7,11<12 ǡɤ 4m+3 Υס
7<11,13<14 ϡ13 4m+1 Υסǡn 7ʾˤʤǤ͡

Ǥ8mϡ4m+4k+1 4m-(4k+1) פ¤4m+4k+3 4m-(4k+3) פ¡ʤɤ 4n+1 4n+3 Υפǿ¡ˤˤʤϤǤ͡
Τʬʤʤޤ(^^;)
ޡ8m פζ 4m оΤˤǿ¤ɽ뤳ȤϸޤäƤǿ¸ߤ 8m ϣĤǿɽäƸ櫓Ǥ
äƤɤζǤ⡢ȾʬοоΤǿ¸ߤиޤ͡

Ĥޤꡢǿϡɤο˴ؤƤоΤΰ֤¸ߤƤ롣ס֥ɥХåϤͽۡ
Ǥ͡
ʡ֤ɤοפϡ4ʾʤǤ

1<2<3,1<3<5 Ϥɡ3<4<5,3<5<7,5<6<7,3<7<11,5<8<11,7<9<11,7<10<13,5<11<17,

äΤȤʤ

59ʲС 21:32:42 MAIL:kennji72001@yahoo.co.jp 27346
uchinyan
#27346
ɥХåͽۤϡʤȻפޤ
Ĥޤꡢǿϡɤο˴ؤƤоΤΰ֤¸ߤƤ롣ס֥ɥХåϤͽۡ Ǥ͡
֤٤Ƥ n Фơn 濴 n-k, n+k ǿȤʤ褦 k n Ȥɬ¸ߤפȤǤС
ɥХåͽۤϾ줿ȤˤʤȻפޤ
Ʊ꤬ͤ̿ޤǤ뤫ɤ

Ʊͤ̿ȤСʤΤ⤢ޤ͡
n >= 6 ʤ뤹٤ƤμϡĤǿ¤ǽ񤯤ȤǤ롣
ΤǽˡɥХåϤ顼˼ͽۤϤǡ顼褯Τ줿̿ȼȤ
㤤ä⤷ޤ󤬡ƱͤʤΤϡǤ͡

դȻפäΤǤ褦̿ꡢ
֤٤ƤζϡĤǿκɽ롣
ϡΤǤ礦
ޤ긫ȤʤΤǤʵ롣ñ˾ǤΤʡ
äȶ̿ꡢ
֤٤Ƥζϡ٤礦Ĥǿκɽ롣
ϡɤǤ礦ˤ̵ʡ
Ǥ⡢ǿʤ֤äƤǤĹޤ͡顢ҤäȤ顢Ȼפä (^^;
ɬ⡢֤Ĺ򤦤ޤȥǤʤǤ͡
Ϥ̵ʡȤ顢ȿ򤦤ޤĤǤ礦
ͥνȡ 510ʿ 9:04:57 MAIL:uchi@sco.bekkoame.ne.jp 27347
⡼ޥ
#27347
>Ʊͤ̿ȤСʤΤ⤢ޤ͡
n >= 6 ʤ뤹٤ƤμϡĤǿ¤ǽ񤯤ȤǤ롣
ΤǽˡɥХåϤ顼˼ͽۤϤǡ顼褯Τ줿̿ȼȤ
㤤ä⤷ޤ󤬡ƱͤʤΤϡǤ͡

n=2m+2 or 2m+3 ɽ뤫ʤǤ͡

>֤٤ƤζϡĤǿκɽ롣
⥷ץDzʵ
ɥХåϤΤƱͤ⤷ޤ͡
ͤƤߤޡ(^^)

⤷Ǥ͡uchinyanͽۡ

510ʿ 1:16:58 MAIL:kennji72001@yahoo.co.jp 27348