ޥ
äܶȤ˻ƥå­äΤ԰¤Ǥ...ߥȤϤޤǤ礦

ȤꤢѷУңѤջѷˤʤ뤳ȤѤˡꤷƤޤ
PowerBook 118ڡ 0:07:31 MAIL:masaru-y@sansu.org HomePage:29121
ʤ
礦֤Ǥ
ޤ顣
118ڡ 0:08:19 MAIL:naka@sansu.org HomePage:naka's Home Page29122
ʸ
Фϡ
118ڡ 0:18:00 29123
ߤ
ѣ£äξ郎ʤäΤǾˣ٤Ȥƺޤޤ
ޤ뤤ǤϤޤ͡ʴˡʤߤˤޤäȤ
Ϥ狼äƤޤ
118ڡ 0:19:58 29124
ޤ륱
ѷУ£Ҥ¤濴˻ˣ١
ѷѣңää濴ȿˣٲžУҡңѤȯ
Ȥϡ٤ȣ٤ȣ٤­Ҥǵޤ

դãĤ餺˲򤱤ƴ򤷤Ǥ
118ڡ 0:36:09 MAIL:take4310@mobile.email.ne.jp HomePage:ޤ륱29125
nishimura
BC˴ؤRоR'ȤȡPBRȢABR'ϹƱˤʤޤ
ޤγ٤Ϸ׻ȡ13٤ˤʤޤ
BAC+BR'C = 43 + (180 - 30 - 13) = 180٤ʤΤǡ
ͳѷABR'Cܻͳѷ߼Ѥ顢BAR'=BCR'=13١
ä60 - 13 = 47٤Ǥ
118ڡ 0:40:49 29126
ʸ
ϤޤäǤ

#29125
ʤۤɡ褯狼ޤ
Ȼפޤ
118ڡ 0:44:13 MAIL:kyorofumi@msn.com 29127
ӣˣ
PBQCĹ3ĺR٤С٤ƱĹȤʤΤǡPRA'77ߣǣ٤Ȥʤꡢ154٤ĺѤȤջѷΤҤȤĤѤ򣶣٤47٤ȤʤꤽǤ͡
118ڡ 0:50:42 29128
⡼ޥ
BC ФRоR'ȤȡABR'CƱ߼Ȥʤꡢ
BRR'ѷȤʤꡢBPRᢤBAR'
BPR=BAR'=BR'C=(180-(180-60-43)*2)/2=13
RPA=60-13=47
ޤǽ񤤤ơäȲ򸫤ȡ
#29126
nishimura ƱǤ͡(^^;
118ڡ 1:25:22 29129
maverick
2Ҥͤ꤯餤äǤ͡
Tokyo 118ڡ 1:31:22 MAIL:tmr6664@gmail.com HomePage:main page29130
ma-mu-ta
Ū˲򤭤äΤǡ߼ѤܻͳѷϻȤ鷺
Ѥ¤Ѥޤ

BCоμȤRоΤR'Ȥȡ
PBRᢤABR'QRCᢤAR'C Ȥʤޤ(ά)
PR=AR'=QRꡢPRQջѷʤΤǡRPA=RQA
BPR+CQR=BAR'+CAR'=BAC=43
ޤCQA=CAQ=180-(60+43)=77ꡢ
RPA+RQA=BPA+CQA-(BPR+CQR)=60+77-43=94
äơRPA=942=47
118ڡ 5:11:21 29131

ϳعΥƥȤ⤢ޤƷˤˤϤ뤳ȤǤޤǤϤϤʤä˲򤯤ȤǤޤǤʵ
118ڡ 9:57:22 29132

ꡧǿؤȣ٤ޤΣĤ­Ȥޤ򤹤٤ƤȤܿˤʤޤξ磶򤿤ƣʤΤǣܿˤʤޤˤǤϣء٤ξȤ⣲ξ粿̤ꤢǤ礦
118ڡ 10:02:28 29133

­ؤȣ٤Ȥ߹碌Ƥ
118ڡ 10:03:52 29134
uchinyan
Ϥˤϡơϡ

ǽ򸫤Ȥϡ֤ء񤷤פȻפäΤǤͤƤߤճȴñǤ ^^v
⡤ѷϤޤפǤϤʤ褦ǡ¦ƱͤջѷǤ⤤褦Ǥ
󡤿ޤΤ褦ʿ޷¸ߤϰϤǤäǤ
޳ѤʤΤǡʲǤϡѷǤϤʤBP = BAABP = 2 * RBC ꤷƲ򤤤Ƥޤ礦

BC ˴ؤ R оΤ S ȤS ABC ȤӤޤޤR AQ Ӥޤ
餫ˡBR = BSCR = CSRBS = 2 * RBC = ABPRCS = 2 * RCB = ACQ Ǥ
BPRBAS ˤơ
BP = BABR = BSPBR = PBA + ABR = RBS + ABR = ABS ʤΤǡBPR BAS Ǥ
ǡRP = SABPR = BAS Ǥ
CQRCAS ˤơ
CQ = CACR = CSQCR = QCA + ACR = RCS + ACR = ACS ʤΤǡCQR CAS Ǥ
ǡRQ = SACQR = CAS Ǥ
ʾΤȤꡤRP = SA = RQBPR + CQR = BAS + CAS = BAC Ǥ
ȡBP = BACQ = CAPAQ Ʊľˤ롤Ȥʤɤ顤
RPA = BPA - BPR = BAP - BPR
RQA = CQA - CQR = CAQ - CQR
RPA + RQA = (BAP - BPR) + (CAQ - CQR) = (BAP + CAQ) - (BPR + CQR)
= (180 - BAC) - BAC = 180 - 2 * BAC
ʤΤǡ
RPA = RQA = 1/2 * (RPA + RQA) = 1/2 * (180 - 2 * BAC) = 90 - BAC
ˤʤޤ
ǤϡBAC = 43 ʤΤǡRPA = 90 - 43 = 47 ˤʤޤ
ͥνȡ 118ڡ 12:41:25 MAIL:uchi@sco.bekkoame.ne.jp 29135
uchinyan
ǼĤɤߤޤ
ޥ뤵λϤȤ⤫ (^^;FAQ ˤäȽ񤤤Ƥޤ͡
ʲäʬʤ⤢긡ƤǤ괺
(ɲäޤ)

#29121
仰ѷУңѤջѷˤʤ뤳ȤѤˡꤷƤޤ
ϤRP = RA λѷУңѡǤ͡βˡ#29135ϡȻפޤ

#29124
ü첽ˤˡ¿ʬABC = 60 Ǥ礦
ξ硤BC//PQ ˤʤꡤΤ˿ޤ䤹Ǥ͡

#29125
ŪڤϤȤ⤫¼Ūˤϡβˡ#29135ƱȻפޤ

#29126#29129
ʤۤɡ߼ѤϡϰϤɤ̯ǤǤǤ͡

#29128
PBQCĹ3ĺR٤С٤ƱĹȤʤΤǡPRA'77ߣǣ٤Ȥʤꡢ
PB QC θ A' Ǥ͡RP = RQ = RA' ϺΥݥȤʤΤǡߤʤ
ʤȤ⡤ABC = 60 ü첽򤹤С餫Ǥ̤ˤϡɤǤ礦
ʤRP = RQ ϡβˡ#29135ʤɤʬޤ
(äɲ)
ʻǤϤʤǤ򤯤ˤϱǤΤ褦ˤƾϤǤޤ
ޤ٤δط顤
BA'C = 180 - A'PQ - A'QP = 180 - BAP - CAQ = 180 - BAP - (180 - BAP - BAC) = BAC
BRC = 180 - RBC - RCB = 180 - 1/2 * (ABP + ACQ) = 180 - 1/2 * (180 - 2 * BAP + 180 - 2 * CAQ)
= BAP + CAQ = 180 - BAC
ĤޤꡤBA'C + BRC = 180 ǤǡA'BCR Ʊ߾ˤޤ
ǡ߼Ѥδط顤BA'R = BCR Ǥ
ˡ#29126#29129ʤɤƱͤˤơBCR = BPR ΤǡRPA' = RA'P ˤʤꡤRP = RA' Ǥ
ƱͤˤơRQA' = RA'Q ⤤RQ = RA' ⤤ޤ
ξǤϡ򤯤ˤϱˤʤäƤޤޤ
R A'PQ γˤʤäƤ롤ȤΤϡ̣Ǥ
(ɲý)

#29131
βˡ#29135ƱǤ
ͥνȡ 118ڡ 15:01:26 MAIL:uchi@sco.bekkoame.ne.jp 29136
ϥ饮㡼ƥ
ǤͤƤǤޤǤ
118ڡ 15:35:58 HomePage:湩ؤĩ29137
⡼ޥ
#29133
ɥХåϤͽۤ1İʾ夢ϤǤ(^^)

A ϴʤΤǡ

ͧhttp://tombow-web.hp.infoseek.co.jp/alacarte/yuai.htm
֣ޤΤˤϡΣĤǤ뤳ȤȯƤޤŻҷ׻Ȥ褦ˤʤäơȯ褦¿οؼԤϤ
ޤߤǤ⣲ĤδȯƤޤ󡣡

ȤȤʤΤǡ餫դA ϡ28 Ǥ͡

28/2=14 ʤΤǡ14 ˤ 11 ޤǤǿΤȤͤФΤǡ13,11 ΤȤ(11,17) Ȥ߹碌ޤ͡

ϡ1̤ꡣ

õˡϤɤФΤǤ礦
118ڡ 15:56:50 29138
uchinyan
#29138
䤬ȤȤΤⲿǤܿǤФΤǡȤϸ¤ʤ褦Ǥ
ͥνȡ 118ڡ 16:35:02 MAIL:uchi@sco.bekkoame.ne.jp 29139
⡼ޥ
#29133,#29139
Ƴ񤷤(^^;

Ƥο A ϡ(1+2+2^2+)(1+3+3^2+)(1+5+5^2+)ɽ뤫顢
A = 2^a*3^b*5^c* ʤ顢
A ¤ϡA*(1+1/2+1/2^2++1/2^a)(1+1/3+1/3^2++1/3^b)(1+1/5+1/5^2++1/5^c)ɽ롣
A ʤΤǡ(1+1/2+1/2^2++1/2^a)(1+1/3+1/3^2++1/3^b)(1+1/5+1/5^2++1/5^c)ˤʤФ褤

1+1/2=3/2
3/2*4/3=2 ϡ2*3=6 ǥᡣ
1+1/2+1/4=7/4
7/4*8/7=2 ϣϣˡ
ΤȤ4*7=28 ʤΤǡ28/2=14 顢11-17 롣1ġ

1+1/2+1/4+1/8=15/8 ϡ15=3*5 ʤΤǡ
Ĥޤꡢ15/8*4/3*6/5=(15*4*6)/(8*3*5)=3ǣϣˡ
ΤȤ8*3*5=120 ʤΤǡ
120/2=60 顢59-61,53-67,47-73,41-79,37-83,31-89,23-97 롣7ġ

1+1/2+1/4+1/8+1/16=31/16 ϡ16*31=496 > 99*2=198 ǥᡣ
ϡ63/32 ǡ63=3^2*7 ʤΤǡ
63/32*13/9*8/7 ϥᡣ
ϡ127/64 ǡ64*127>198 ǤʾϤʤ

1+1/3=4/3 ϡ4=2^2 ʤΤǡ
4/3*7/4 ǥᡣ
1+1/3+1/9=13/9
13/9*14/13 ǥᡣ
1+1/3+1/9+1/27=40/27 ϡ40=2^3*5 ʤΤǡ
40/27*15/8*6/5=(40*15*6)/(27*8*5) ϥᡣ
1+1/3+1/9+1/27+1/81=121/81 ϡ121=11^2 ʤΤǡ
121/81*133/121=(121*133)/(81*121) ǥᡣ
ʾǤϡʬ줬 81*3=243>198 ǥᡣ

1+1/5=6/5 ϡ6=2*3 ʤΤǡ
6/5*3/2*4/3 ǥᡣ

1+1/5+1/25=31/25 ϡ25*31>198 Ǥᡣ
ʬϡ125 ʤΤǡ125*2>198 ǡ⤦ʤ

1+1/7=8/7 ϡ8=2^3 ʤΤǡ
8/7*15/8 ǥᡣ

1+1/7+1/49=57/49 ϡ57=3*19ʤΤǡ
57/49*4/3*20/19=(57*4*20)/(49*3*19) ǥᡣ
ʾǤϡ49*7*2>198 ǥᡣ
1+1/11=12/11ϡ12=2^2*3 ʤΤǡ
12/11*7/4*4/3 ǥᡣ
1+1/11+1/121=133/121 ϡ2*121>198 ǥᡣ

1+1/13=14/13 ϡ14=2*7 ʤΤǡ
14/13*3/2*8/7 ǥᡣ
1+1/13+1/169 ϡ2*169>198 Ǥᡣ

1+1/17=18/17 ϡ18=2*3^2 ʤΤǡ
18/17*3/2*12/9 ǥᡣ

Ρ17*17=289 ǡ198 ʾˤʤΤΤϤʤ

17 ʾǿϡƱͳǡ19*20=380>198ˡ⤦ʤ

ɡ1+7=8Ĥʡ (^^)V

⤷Ǥ͡礵ΥꥸʥʤǤ
äȥޡȤ˸Ǥ͡(^^;

119ʶ 9:42:47 29140
Shin Koba
uchinyanءľŪޤ֤޷򥤥᡼RBRCRBQCؤοľʬˤʤȽǤޤ°פ˲᤮ơߤޤ󡣲ȤߤäȤʤ¤ǡٶƤޤuchinyanξ򸫤ơ

118ڡ 22:14:12 29141
uchinyan
#2914
RBRC PBQC ľ򤹤ˤϡPBR = 90 ɬפʤΤǡABR = 30 ǤʤФʤޤ󡣤ˤ ABC = 60 ɬפˤʤޤ
ƤΤȤˤϡΤ˿ľʬˤʤäƤޤ
ΰ̣Ǥϡü첽βˡäȤǤ͡
R A'PQ γˤʤ뤳Ȥϡ#29136ɲʬǼȤŪˤ褦Ǥ
򤤤Ȼפޤ餳ٶˤʤޤ ^^
ͥνȡ 118ڡ 23:34:34 MAIL:uchi@sco.bekkoame.ne.jp 29142

ޤ󡣥⡼ޥ󤵤󡣤ĤפĤ񤤤ƤΤǤȤäˡϼʬǤ褯狼ޤ󡣤ʤߤ˺ϣ̤ǤäƤޤ
119ʶ 16:45:49 29143
ޤ륱
ɽ裸̡ޥ뤵פäơ
119ʶ 17:37:30 MAIL:take4310@mobile.email.ne.jp HomePage:ޤ륱29144
⡼ޥ
#29143
礵ء
פĤʤǤ(^^)
ɤäդ꤫餽פĤǤ礦
äȶ̣ޤ褫ä鶵ƲOrz
ǹäƤäƤΤϡԥ塼dzǧ줿äƤȤʤǤ
ΤꤿȤ(^^;

ͧͤ¬줿¬ƤߤƤäƤ줿ȤǤʤѤǤ硩äơʬäƤʤΤˤ(^^)
119ʶ 19:39:42 29145
Ѥ
߼ѤȤޤ
ɤ֤!!ޥ뤵פɤߤʤäƤޤ
ɤ⤦Ȼפޤ
֡ 119ʶ 20:37:22 HomePage:ʥڡ29146

ͧãͤФƤΤ褦ʤΤǤ褯ñФƤΤǤ⤷Ȼפä򥢥󥸤ƤĤäƤޤʤߤͤΤϻ֤򤫤ƽ֤˲򤤤Ƥ椱ФΤǤΤФǤ̤Ȥ⤹٤Ƥ̤񤭽ФǡǧƤޤʤμȤǵ˻פäȤ򥢥󥸤ˤޤ褫äȤƤߤƤ
119ʶ 22:49:13 29147

ꡧɽΤϵ夬ۤμ򣱼ʸžˤΤˤ֡1ǯˤˤȤۤμ򣱼Τˤ֡ǯˤɽƤޤ
ϵ塡
ŷ
ʤޤǷ׻ǽФ䤹뤿οǤΤʤΤǤϤޤ󡣡
ǤϺǽ餬ν֡ʿϲŷˤۤޤľˤʤäƤȤˣľˤʤΤϲǯ夫ʲȤʣˤʤΤDzǯȤȤǹͤƤˤޤΤȤ֤ˤȤɤդˤʤ뤫ۤɬդˤȤϤޤ衣
119ʶ 23:06:17 29148
maverick
#29144 ֵ ޥפ轵黲äƤޤ衣տޤϤ褯狼ʤΤǤޤȤפޤ󤷡

edit: ⤷ѻȤä᡼ٱΥƥȤΤޤ͡
Tokyo 120ڡ 1:31:44 MAIL:tmr6664@gmail.com HomePage:main page29151
ԥ饹
#29148
ǯʤѤǤޤ
֤ϳŷڡڡСϡ⡢塢ۤǤ
120ڡ 1:27:10 29152
⡼ޥ
#29148
180٤Ǥ⤤Τǡ0.125,0.3,1/2,1,6,15,42,82.5 ǯȾ롣
ޤ礭ͤ롣82.5 42 Ȥθܿϡ3*4*7*55 ǯ
ϡ15,6,1,1/2,3/10,1/8 dzΤǡ3*4*7*55=4620 ǯ롣

3*4*7*55/165=28,/84=55,/30=/2*3*5=2*7*11,/12=7*55,/2=2*3*7*55,/1=3*4*7*55,/(6/10)=2*7*55*10,/(1/4)=3*4^2*7*55 ƤꡢǽƱ
ŷڡڡСϡ⡢塢ˤν֡

äȴñ˽Ф͡ (^^;

164ǯθžä顢8610ǯǡ
ڤʬ2;뤫顢ŷڡСϡ⡢塢ˡڡνˤʤäǤ͡
120ڡ 2:22:30 29154
maverick
#29154 Ⱦʬ2310ǯʤǤ
ŷȿ¦Ǥ

ְäʡ

Tokyo 120ڡ 2:28:54 MAIL:tmr6664@gmail.com HomePage:main page29155
⡼ޥ
#29155
maverickءOrz
Ǥ͡84 165 κǾܿȾʬǤΤ
Ǥ⡢ȸˤϤɤФΤʤ

2310ǯ=2*3*5*7*11 ɡ2^2 ڡŷȿ¦ʤ
ɡ
ڡСϡ⡢塢ˡڡŷ ν֡

120ڡ 2:36:40 29156
maverick
#29156 ⡼ޥ󤵤󡢾κǾܿäƤΤ祤ʤäΤ2dzäƤߤΤǤ2^2ʼԤǤ͡
Tokyo 120ڡ 3:00:34 MAIL:tmr6664@gmail.com HomePage:main page29157

maverick󥹥⡼ޥ󤵤󤪤ߤȡȿФˤ⤯ȤΤߤǤ(^^) ߤϤۤȤϵ夫鸫ۤΤۤ¾ľˤʤꤽ餷Ǥʹá

120ڡ 4:20:35 29159
ma-mu-ta
#29148 ˡ
ǯñ̤ǹͤΤ顢ϵθž1ǯꡢľˤʤΤϡ
줾Ʊȿ¦ȤȤʤޤ
ޤ礭ŷȳۤȰľˤʤȤͤޤ
ŷΤ84ǯǡ84165κǾܿ4620ǯ塣
ŷȿ¦Τϡǽ餬42ǯǤȤ84ǯˤʤΤǡ
8442=2ꡢ462022310ǯ塣(231042)8427ȿ¦
äơ˰ľˤʤΤ2310ǯȹͤơ¾Ĵ٤ޤ
23103077
231012192.5(23106)12192ȿ¦
231021155ϵ231012310
23100.6385023100.259240
ʾꡢ˰ľˤʤΤ2310ǯǡڡСϡ⡢塢()ڡŷν֤Ȥʤޤ

ɵ򤽤äΤǤäƤߤޤ٤ä褦Ǥ͡
120ڡ 5:12:15 29160
⡼ޥ
#29159
礵ء
⤷ͤĤޤ͡(^^)

#29160
ma-mu-taء
ͤǤޤ꤬ȤޤOrz

ͭ̾餷ˡͧͤ
3*3*3Υ塼֡ʥ롼ӥå塼֡ˤǤ
27Υ塼֤ʬȤ顢㲿
դ뤨Ф褤Ǥ礦äʬ
ۤʬξ֤ơ1٤ˤ
äƤ褤Ȥޤ
120ڡ 5:10:24 29161
⡼ޥ
δΤʤΤ̤餷
ξ

ȤʤˤʤäΤǡƶڤСʤޤ(^^;

#29140 Υ르ꥺǹͤȡ

ʬ줬2λʬҤϴʬҤǰɬǿʤΤǡǿʬʬҤϡη֤
3/2*4/3=2
7/4*8/7=2
ǡ(2^m-1)/2^(m-1)*2^m/(2^m-1)=2 顢2^m-1 ǿλʤ
2^(m-1)*(2^m-1) ϴȤ롣

(2^m-1)/2^m 2^m-1 λϡĤǰʴǿˤʬ򤵤졢/ǿ^/ǿ^γݤ 2 ˤʤʤȤʤ
/ǿ^򣲤İʾĤȡʬ 2^m ΰҤɬפȤʤꡢǤϤʤʤ롣
1Ĥʤϡ餫ˡ/ǿ^Ѥη֤Ǥʤ
ǤϡѤϴʤΤǡ2ˤϤʤꤨʤ

顢1Ĥ/ǿ^ꡢȤϡ/ǿ^Ѥλ
⡢/ǿ^ζϡ21ĤΤΡ
ǿϡ4m+1 ȡ4m-1 ʤΤǡ
4m+1 ϡ
1+1+1+1=4 顢3,7,11,ǿ4k-1 ΤΤϡ2^2 ĤΤŬ
4m-1ϡ
1-1=0,1-1+1-1=0 ʤΤǡ2^2 Ŭ

äơ4m+1 ǿΤ(4k+1) ΤΤͤФ褤
1+(4m+1)=4m+2 ΤȤ4m+2=2*(2m+1) ʤΤǡ2m+1 ǿǿѤʬ礬롣

2m+1 ǿλ
/ǿ^ǤʤФʤʤʬϤδǿϺ2Ĥ뤬ʬҤˤ1ĤʤΤǡڤʤ

2m+1 ǿѤʬ
/ǿ'^*/ǿ''^ȤʤꡢʬҡʬδǿοʤΤdzڤʤ

1+(4m+1)+(4m+1)^2+(4m+1)^3+(4m+1)^4+(4m+1)^5=4M+6=2(2M+3)
2M+3=2m'+1 ǡƱͤΤȤ롣

̤ˡ4M+6+4k=4M'+6=2(2M'+3) ʤΤǡƱͤΤȤڤΤʤ
Ĥޤꡢ¸ߤʤ

120ڡ 13:29:07 29162
ߤ
#29161˥⡼ޥ󤵤
ǤΤʡο褬ޤʬƤơǤƱ
ʿ̤̤ȤΤʤ̤ɡ
120ڡ 13:57:30 29163
uchinyan
ءޤäȸʤ֤ˤ夬Ǥͤˤ衤뷿Τ褦ǡˤϤĤƤʤ(^^;

#29148
礵ϡ줾ϣǯդꡤ
4 * 360 = 8 * 180
5/3 * 360 = 10/3 * 180
ϵ塡1 * 360 = 2 * 180
1/2 * 360 = 1 * 180
1/12 * 360 = 1/6 * 180
1/30 * 360 = 1/15 * 180
ŷ1/84 * 360 = 1/42 * 180
1/165 * 360 = 2/165 * 180
ʤΤǡǯñ̤ǹͤ餷顤줾줬ǡ180٤ܿˤʤ褦ˤФǤ
ξκǾϡ餫ˡʬ 361542165 κǾܿ11 * 7 * 6 * 5 = 2320 ǯǡ
ΤȤϵۤľ鸫
0 ١פ 180 ζ
0 ١פ 180 ζ
ϵ塡0 ١פ 180 ζ
0 ١פ 180 ζ
180 ١פ 180 δ
0 ١פ 180 ζ
ŷ180 ١פ 180 δ
0 ١פ 180 ζ
ʤΤǡΤˡȡŷȿ¦ޤ͡

#29161
⡼ޥ󤵤Υ롼ӥå塼֤Ǥϡ
ʥ֤ˤϡबʤäƤʤ¤ꡤΥ塼֤γ̤ڤФΤˣɬפʵǤ
ޤʴŤʤΤǤ礦 (^^;
ǤǤ뤳Ȥ餫Ǥ礦

#29162
⡼ޥ󤵤δäϡȤäƤ륢르ꥺब褯ʬäƤʤΤǡǤϤ褯ʬޤ
ϡ̤Ǥ顤Ť˶̣ɬפꤽǤ
ͥνȡ 120ڡ 14:12:57 MAIL:uchi@sco.bekkoame.ne.jp 29164
uchinyan
#29162⡼ޥ󤵤δ
äȸƤ褯ʬʤȤ
/ǿ^򣲤İʾĤȡʬ 2^m ΰҤɬפȤʤꡢǤϤʤʤ롣
֤ɤΡʬ졩
2^m ΰҡפȤϡιԤ
(2^m-1)/2^m 2^m-1 λϡ
2^m äȤ⤳μʬ 2^(m-1) Ǥϡ
ִǤϤʤʤפȤϲ
1Ĥʤϡ餫ˡ/ǿ^Ѥη֤Ǥʤ
䤳ǤϡѤϴʤΤǡ2ˤϤʤꤨʤ
Ϥ褵Ǥ͡

ϡ꤬⤢ޤ4m+14m-1 ʬषƲ򤷤ʤǤ

äơθݤ褯ʬʤǤ

ʤ⤦ߺդƤʤȡ
ͥνȡ 120ڡ 14:42:52 MAIL:uchi@sco.bekkoame.ne.jp 29165

ꡧۤξʤϤޤ
УѤȣĤζޤФ飱ĤζοˤޤʶϤ٤ƣУѤʿԤǤˤΤȤȣУѤδ֤γ٤ˤʤޤ
θȿͤƣУѤ̲ᤷƣܤζοˤޤܰʹߤϣФ飱ζޤǤθ̤äΥʬУѤΥƤޤ
ʣФ飱ܤζޤǤѤȤȣܤζȣУѤϣʿԤΥƤޤ
ޣܤȿͤȣУѤθʣѡˤǤޤ
УѤĹΤȤϣФѤޤDzѤǤ礦
ޤФΤǤΤ狼ˤοޤ줿ȻפäƤ
줤ʿߤĤʤƤޤȾˤʤߤʤȤĤ⤷ޤ󡣺ϣĤ뤳ȤǤޤʴ

121 11:50:16 29166

ˤʤΤϺǽˤǤ뻰ѷʣСܤζǽθȣУѤθˤѤȤƤ
ˤޤǤ
120ڡ 16:24:38 29167
⡼ޥ
#29165
uchinyanء
˻äơդˤϤֻǤʡˤȻפޤ
르ꥺϡ#29140 ΤΤȤäƹͤޤ

#29166
ޤʬɤƤʤǤ͡(^^;
ʤʸƤʤǤ
鿲ƤʤΤǡ
ꥢʡʡƬǥ󥸤Ƥߤޡ(^^)
120ڡ 18:48:39 29168
maverick
#29166 礵 䤬ɤǤ(Ʋ򤤤Ƥ)PǽζޤǤθεΥxȤ5Ĥζޤ139x,Qޤ217xεΥʤǤ729964Ȥ217dzڤʤǤ(3/2ȤäƤɤƤȾüʿˤʤޤ)ɤ߰㤨Ƥޤ

Ǽ䤷ꤷơ
Tokyo 120ڡ 21:10:25 MAIL:tmr6664@gmail.com HomePage:main page29169

ޤ󡣼ʬη׻ߥǤΤʿޤ
121 10:43:57 29171

Ƥޤ29166򸫤Ƥ
121 11:51:03 29173
⡼ޥ
#29165 uchinyanء

٤ʤޤ

/ǿ^򣲤İʾĤȡʬ 2^m ΰҤɬפȤʤꡢǤϤʤʤ롣
>֤ɤΡʬ졩2^m ΰҡפȤϡ

Υ르ꥺफ餤ȡʬҤ˶ФƤȡǤäˤϡ(1+1/2)ʾΤΤɬפˤʤΤǡĤޤϡǰ2ĤȤˤʤǤʤʤȤȤǤ

>ιԤ
(2^m-1)/2^m 2^m-1 λϡ
> 2^m äȤ⤳μʬ 2^(m-1) Ǥϡ

ϡŦΤ褦ˡͤƤ顢̣ʤȤäƤޤ͡OrZ

>ִǤϤʤʤפȤϲ

ǽΰ̣ǤʬҤ˶ΤΤ2İʾȡ1Ĥʬ2ɬסʬǿݤΡʹͤƤ봰θˤ϶

1Ĥʤϡ餫ˡ/ǿ^Ѥη֤Ǥʤ
䤳ǤϡѤϴʤΤǡ2ˤϤʤꤨʤ
>Ϥ褵Ǥ͡

>ϡ꤬⤢ޤ4m+14m-1 ʬषƲ򤷤ʤǤ

ǿϡ
1+1/3=4/3
1+1/3+1/3^2=13/3^2
1+1/3+1/3^2+1/3^3=40/3^3 ȡʤ顢ʬ줬ʤʬҤ϶ʤʬҤϴˤʤäƤΤǡǿζͤФȤˤʤꡢ
áä̤ǿʬɬפʤựʤǤ͡Orz

ȤȤϡ
/ǿ^*/ǿ^*/ǿ^*=2 ˤʤ뤫ȤȤǤ
ʬҤ˽ФƤϡʴǿʬȰۤʤǿˤΤϤ
ʤʤ顢1+1/p+1/p^2+1/p^3+ +p^n :n ϶ϡ
(p^(n+1)-1)/(p^n*(p-1))=(p^n-p^(n-1)+p^(n-2)-+1)/p^n ʤΤǡˤϤʤʤ

ǽζ/ǿp^衡򾯤ʤȤˤ뤿ˤϡʬҤζ=2*ǿq*ǿr*Ρ
δǿˤϡʬδǿϴޤޤʤ顢Ѥˤʤ뤿ˤϡʬҤ˺ǽʬδǿĦĤޤꡢ/^ȤҤݤʤФʤʤ
ǰʤ顢Ԥͤޤޤ(^^;

ޤͤƤߤޤäOrz
121 16:40:17 29174

ҥȡ٤Ƥλѷʴطˤʤޤ
121 15:33:46 29175
⡼ޥ
#29166 ȿ
PQ*2/6*2/3*PQ/3*1/6*1/2=PQ^2/543?
㤤Ƥ뤫ʡ
121 17:03:57 29176
⡼ޥ
#29166 ^2

ǽλѤդĹ1
λѤա1*2=2
ϡ(1*2+2)*2=8
((1+2)*2+8)*2=28
((1+2+8)*2+28)*2=100

Ĥޤꡢ1+2+8+28+100=139
139*k=PQ
뻰=2k*2k/3/2=2k^2/3=2*(PO/139)^2/3
ǡ3 ФƤ褦Ǥ

ޤդɤ߰㤨Ƥ뤫(^^;
121 23:22:03 29178
maverick
#29166
ǽζޤǤxȤ5ܤζޤ178xäƤޤޤ(㤦 ְ㤨Τʡߤޤ)
εΥx,3x,10x,36x,128xǷ178xǤPQ餽줾ζޤǤεΥ1/2x,x,4x,14x,50xǤ餫˥⡼ޥ󤵤Ȥ㤦ʤ󡣤Ǥ⤤ˤǸˤϢ3ǤƤޤ͡

Tokyo 122ʷ 0:16:50 MAIL:tmr6664@gmail.com HomePage:main page29180
uchinyan
#29166
ͤƤߤޤ
ǽζޤǤ x ȤȡP 飵ܤޤǤζΥϡmaverickƱ
ľPQϡk = sqrt(3) * x Ȥơ⡼ޥ󤵤Ʊ
Ȥʤޤ
ˤ衤礵㤤դäƤʤǤ礦
ͥνȡ 122ʷ 11:25:43 MAIL:uchi@sco.bekkoame.ne.jp 29181
⡼ޥ
δ(^^;ǶߤΤǤ

m p ǿȤȤ
2*m^2=1+p+p^2+p^3++p^(2k-1)
褦ʤȤޤ͡

줬ʤȤС
δʤȤΰΤͤˤʤꤽʤǤ(^^)
122ʷ 17:33:45 29182
uchinyan
#29183
Ϥꡤ礵ְäƤ褦Ǥ衣褯ǧƤߤƤ
ͥνȡ 122ʷ 21:03:14 MAIL:uchi@sco.bekkoame.ne.jp 29184
uchinyan
#29182
ȡ
2 * 3^2 = 18 = 1 + 17
ͥνȡ 122ʷ 21:07:26 MAIL:uchi@sco.bekkoame.ne.jp 29185
⡼ޥ
#29185
uchinyan󡢤꤬Ȥޤ
(^^;

ΤȹͤƤǤ

2*q^/p^ǽȤȡ

ִñʾ硢2*q^2/p ͤ롣

2*q^2/p ˡp/q^2 ݤУȤʤȤ

2*q^2=1+p
p=1+q+q^2

ƤϤ

Ĥޤꡢ

2*q^2-1=1+q+q^2 顢
q^2-q=q(q-1)=2 Τϡ(p,q)=(7,2) 顢ǿǤϤʤ

2*q^2m/p^(2k-1) ϡ

2*q^2m=1+p+p^2++p^(2k-1) ȤȤ顢

ޤ褦p,q ΤäƤȤޤꡣ

ϡuchinyan󤫤顢¸ߤϾʤȤĤϤ뤳ȤŦޤΤǡ

Ĥϡְ°פʾȤơ
p^(2k-1)/q^2m Τ뤫

Ĥޤꡢ

p^(2k-1)=1+q+q^2++q^2mʤǤ

Ĥˡ

2*q^2a*r^2b*/p^(2m-1) ΤΤϤޤäƤ뤳Ȥˤʤꡢˡ/q^2a,/r^2b,Ѥͤ뤳ȤȤʤ롣ΤȤ** = p^(2m-1)*ˤʤʤȤʤġ=s^2a'*t^2b'*,=u^2c'*v^2d'*ǤʤȥᡣǤʤȡs,t,u,v ʴǿǤǤȡǤäʬˤοʴǿ^ɬפˤʤ뤿ᡢλʬ;ʬ2뤫顣
ȤȤϡs,t,u,v ϡʴǿȤȡp ޤޤʤȤˤʤꡢξڤʤ
ʴǿǤʤȤȡ p ˤʤϤ
Ĥޤꡢ=p^x,=p^y,
x+y+=2m-1
p^x/q^2a,p^y/r^2b, ȤФ褤
ʤ顢
1+q+q^2+q^3++q^2a=p^x
1+r+r^2+r^3++r^2b=p^y Ʊ˸ʤФʤʤ
ޤ2*q^2a*r^2b*/p^(2m-1)ʤΤǡ
1+p+p^2+p^3++p^(2m-1)=2*q^2a*r^2b*ˤʤʤȤʤ

ʤơť¤Τ褦ʤȤͤƤޤ(^^;;
122ʷ 22:37:20 29186
粬ҹ
פ֤ޤʡϸĿŪˤϾǤ
գ£ä򼴤ˣҤȿ¦ˣҡǤ򤪤ޤ£ңҡǤѷʾάˢ£УҢᢤ£ҡǡäƢܣңУ᣶ݣᣴ
ϢУңѤջѷˤʤäƵޤΤȹֹͤͤƤǤޤǤʡפ֤Ƭ餫ʤäޤ
122ʷ 22:52:46 MAIL:toshi009@land.hokuriku.ne.jp 29187
粬ҹ
԰¤ʤΤǡǼ䤷ޤޥ뤵νصǯܺäϤޤϤ̵褦ʵʡ
122ʷ 23:11:32 MAIL:toshi009@land.hokuriku.ne.jp 29188
⡼ޥ
δε

ϤǤ˾ƤΤǤ
錄Υ르ꥺǤȡ

δ
ǿ/2^m*2^(m+1)/ǿʤ顢=2 顢
ǿ=1+2+2^2+2^3++2^m=2^(m+1)-1 ǤС
2^(m+1)-1 ¤ϡ1+2^(m+1)-1=2^(m+1) Ǥ뤫顢Ω
λδϡ2^m*(2^(m+1)-1)

p*q/2^m*2^a/p2^b/q ΩĤȤȡ
2^a=1+p
2^b=1+q
a+b=m+1
ΩʤƤϤʤʤ

2^a=1+p 顢p=2^a-1
2^b=1+q 顢q=2^b-1
p*q=1+2+2^2+2^3++2^m

p*q=(2^a-1)*(2^b-1)=2^(a+b)-2^a-2^b+1=2^(m+1)-2^a-2^b+1 줬
1+2+2^2+2^3++2^m=2^(m+1)-1 ʤƤϤʤʤ
2=2^a+2^b ˤϡa=b=0 λΤߡ
Ĥޤꡢp=0,q=0 Ȥʤ̷⡣
餯ʬҤδǿοƤƱȤϸǤ͡
äơ2^(m+1)-1 ǿλΤߤ 2^m*(2^(m+1)-1)

줬δ¸ߤ˵ޤ񤷤ʤΤϤʤʤǤ礦(^^;

顼ϤɤΤ褦˾줿ΤgoogäƤʬʤ(^^;

ޤǽ񤤤ơp^2a*q^2b*/2^m λϤɤʤäƤȤϸƤʤΤ˵դꤷơ(^^;;
ޤͤƤߤޤOrz
123ʲС 0:28:58 29190
ޥ
#29188

ϤϤƤޤǡռǤֿä褦ʵ1/8,9,10ˤǤϤƤޤ(^^;
PowerBook 123ʲС 13:02:56 MAIL:masaru-y@sansu.org HomePage:29192
uchinyan
#29190
δ

顼󤬤ɤΤ꤫ǤϤޤ󤬡˹ͤȤޤ
ְäƤ뤫⤷ޤ󤬡Τ褦ˡŪñˤǤޤ

a δȤޤ
a ϶ʤΤǡn 1 ʾb Ȥơa = 2^n * b Ƚ񤱤ޤ
ǡ c ¤ s(c) ɽȡ2^n b ȤϸߤǤʤΤǡ
s(a) = s(2^n * b) = s(2^n) * s(b) = {2^(n+1) - 1} * s(b)
ǡa ϴʤΤǡ
s(a) = 2 * a = 2^(n+1) * b
Ǥǡ
2^(n+1) * b = {2^(n+1) - 1} * s(b)
餫ˡ2^(n+1) 2^(n+1) - 1 ȤϸߤǤʤΤǡk 1 ʾȤơ
b = {2^(n+1) - 1} * k
Ȥʤޤ
ǡk 1 ǤʤȤȡb ϡʤȤ⡢
1, k, 2^(n+1) - 1, {2^(n+1) - 1} * k
Ȥޤǡ
s(b) >= 1 + k + {2^(n+1) - 1} + {2^(n+1) - 1} * k = 2^(n+1) * (k+1)
ǡ
2^(n+1) * b = {2^(n+1) - 1} * s(b) >= {2^(n+1) - 1} * 2^(n+1) * (k+1)
b >= {2^(n+1) - 1} * (k+1) > {2^(n+1) - 1} * k
ǡ{2^(n+1) - 1} * k = b ʤΤ b > b Ȥʤꡢ̷Ǥ
ǡk = 1 ˤʤꡢ
b = 2^(n+1) - 1
ˤʤޤ
ǡb ǿǤʤͤƤߤޤ
ȡ1, 2^(n+1) - 1 ʳΰ d, e, de = b ꡢۤɤƱͤˡ
s(b) >= 1 + d + e + {2^(n+1) - 1} > 2^(n+1) + d
2^(n+1) * b = {2^(n+1) - 1} * s(b) > {2^(n+1) - 1} * {2^(n+1) + d} = 2^(n+1) * {2^(n+1) + d} - {2^(n+1) + d}
b > 2^(n+1) + d - 1 - d/2^(n+1) = {2^(n+1) - 1} + d * {2^(n+1) - 1}/2^(n+1)
Ȥ2^(n+1) - 1 = bd/2^(n+1) > 0 ʤΤǡ
b > b + d * b/2^(n+1) = b * (1 + d/2^(n+1)) > b
̷Ǥǡb = 2^(n+1) - 1 ǿˤʤޤ
b = 2^(n+1) - 1 ǿΤȤ a = 2^n * {2^(n+1) - 1} ˤʤ뤳Ȥϡ餫Ǥ͡

ɡδϡ
2^n * {2^(n+1) - 1} 2^(n+1) - 1 ǿ
ȷޤޤ

ξǤϡ2^n, 2^(n+1), s(2^n) = 2^(n+1) - 1 ޤ˸ƤΤݥȤˤʤäƤޤ
ξϡǰʤ顢Ϥʤǡ꿼ͻɬפˤʤ褦˻פäƤޤ
ͥνȡ 123ʲС 15:05:42 MAIL:uchi@sco.bekkoame.ne.jp 29193

ˤޤǤʵˡʬٶ­Ǥȿʡˡ롦룹ʤ飱3ˤʤޤϸƹͤƤޤ
123ʲС 16:52:02 29194
⡼ޥ
#29193
uchinyan󡢤꤬Ȥޤ
ǼǤ
ta
ˤΥʥǤϡˤŬˤǤ͡(^^;
123ʲС 18:29:01 29195
maverick
ǤؤǤǤ͡ΤäƤñΤʤǺǤ
1/sqrt(1+x^2)ʬƤִʬǤ㣲̤ꤢޤǷ빽Ǥ

edit: ȤߤȡΤä⤤Ƹʤ
edit2: TeXȤʤ
Tokyo 123ʲС 23:39:51 MAIL:tmr6664@gmail.com HomePage:main page29196
uchinyan
#29194
ϡ򤯤Ϥ뤫񤷤ȻפޤǤ⡤ʬٶˤʤ뤳Ȥ¿Ȼפޤ
줫פդҲ𤷤Ƥ͡
ʤߤˡϡĿŪˤϡȤƤ⤤ȻפäƤޤ ^^/
ͥνȡ 123ʲС 21:12:23 MAIL:uchi@sco.bekkoame.ne.jp 29197
粬ҹ
#29192
Ϥǧޤʡˡ
ʤߤ˽褬ɤ⤷ޤ󡣻֤ä
124ʿ 22:56:18 MAIL:toshi009@land.hokuriku.ne.jp 29198
ݤ
٤ߤʤ͡
⤦Ǽ򡣥դɸ³
äѤ餤ŷ񡡡 124ʿ 23:38:35 MAIL:hopes@mba.ocn.ne.jp HomePage:HOPES褤Ȥ٤Ϥ29199