ޥ
ԤФä褿褦...¿ĤĤޤ

졢ϤäƤȤˡ֤դȡ׻פ⤫˥ꥸʥǤ֤ɤˤ뤫פǾǺߤޤŪʥǥϤǽޤ(^^;

ȤꤢߥʤɤΤǤ...
422ڡ 0:31:51 36125
ͣ.ǥ
ꡢģ////ӣ¡ң//ģ//ãС
ģ¤ȣäθǤȤ
ǡǣãУġģá¡£С11
ģǡǣ¡12£ǣҤʿԻշˤʤ뤳ȤȤä
ңȡȣ¡23
ңԣġᢤң£á(1/2)(2/5)(1/5ˢң£á(1/5ˢ£ã
ȵޤ
422ڡ 1:08:34 36126

褦ʲˡǤ
APQSȤȢABCܢACQᢢABCDS/2
SB//AC//DQQCCB1:2ʤΤDAAS1:2
ꢤDACS/6 ASCS/3
AR//BD//PCPBBA1:1ʤΤCDDR1:1
ART梤DBTǢRDBᢤDCBS/4 RDAᢤDACS/6
ʤΤ2:3äATTD2:3
RTDᢤRDA*3/5S/6*3/5S/101/5*S/21/5*ABCD
422ڡ 1:48:46 36127
abc
Ʊ褦ʲˡǤ

ͳѷABCD=BCR=DAPꡡDBRACPĭRD:DC=AB:BP=1:1ĭ
ޤACQ:ABC=1:2ǢACQ=DAC(ͳѷABCD=ABQ)
BDACθEȤ
DE:EB=1:2ĭ
DT:AT=BD:RA=3:2ĭ
ꢤRDT=DAC*3/5=(ͳѷABCD*1/3)*3/5(譣)
=ͳѷABCD*1/5()

ǤʤʤͳѷABCD=CDSξɬפʤΤǤϡ)
422ڡ 11:45:06 36128
ޥ
#36128 abc
> ʤʤͳѷABCD=CDSξɬפʤΤǤϡ)

Ϥ̤Ǥ¤顢ֻͳѷPQRSѤפȤˤƤΤǤʿͳ˲򤱤뤳Ȥľ˵դޤơѹȤаޤޤ..̾ĤȤƻĤäƤޤޤm(__)m
422ڡ 11:04:13 36129
uchinyan
Ϥˤϡơϡ
ʤʤȻפޤʴǡ

AC BD θ O Ȥޤ
ABCD = DAP DB//CP ǡAOOC = ABBP = 11 Ǥ
ABCD = ABQ AC//DQ ǡBOOD = BCCQ = 21 Ǥ
ABCD = BCR DB//RA ǡCDDR = COOA = 11DORA = 12 Ǥ
ǡRABD = RA(BO + OD) = 2(2 + 1) = 23 Ǥ
ޤDB//RA TRA TBD ʤΤǡATTD = RABD = 23 Ǥ
ǡ
RDT = BCR - TBCD = ABCD - TBCD = TAB = DAB * 2/5 = ABCD * 1/2 * 2/5 = ABCD * 1/5
ˤʤޤ
ͥνȡ 422ڡ 12:08:59 MAIL:uchi@sco.bekkoame.ne.jp 36130
⡼ޥ
ä...^^;
㤤Ƥ...
9t^2-4t^2=5
...4t^2-t^2=3
3-2=1
1*((1+3)/(1+3+1))=4/5
4/5 : 4 = 1 : 5
ХǤ...Orz...
422ڡ 12:43:14 36131
uchinyan
ǼĤɤߤޤ
Ѥ狼顤
AC//QD(//SB)BD//PC//RA ȤȤȡATTD = 23 򼨤ȡ
ϳƱ褦Ǥ
δ֤ϡ

#36126
AC BD θ G Ȥ AGGC = 11DGGB = 12 ƳABGR ʿԻշˤʤ뤳ȤȤˡ

#36126
APQ ˤ濴˹ͤˡ

#36128(¿ʬ)#36130
AC BD θ O Ȥ AOOC = 11DOOB = 12 ƳTRA TBD Ȥˡ

#36131
ؤˤˡΤ褦Ǥܺ٤

פäΤǤ꤯ɤǤO CRB νſʤΤǡRB AC θ E ȤȤ AEEC = 13 ǡ
줫顤ͥ饦 ATTD = 23 ФʤƲˡ⤢ޤ͡
ͥνȡ 422ڡ 13:03:02 MAIL:uchi@sco.bekkoame.ne.jp 36132
⡼ޥ
#36131
CRαĹȡPAαĹǤǤ뻰Ѥǹͤޤ
RA//DB//CP
DBPC=5
RABD=3
DT:TA=4:1
DRA=1
DRT=1*(4/5)
DABC=4

ޤ...^^;v
422ڡ 14:03:17 36133
⤬Ф
693ꡢ
3/(6+9)Ǥ͡(С
58 422ڡ 18:03:50 HomePage:YoutubeǤ36134
wowka
1:4ΨDzȤƤΤǤ㤦褦Ǥ
422ڡ 19:59:33 MAIL:takatu@iris.ocn.ne.jp 36135
fumio
䡼⤷äǤѷѤޤ
Ȥ⤵󤹤
ǤϤޤ͡
423ʶ 5:59:31 36136
fumio
ǯ奪եߤϻ700ǰפͤƤޤ͡
ڤߤˤƤޤ
423ʶ 6:06:20 36137
ޥ
#36137
ʤǤ󤪵٤ߤˤɤäΤ...ʡʳǧƤʤ

⤦٥ʥ󥹡6/20ˤǥեߤ»ͽǤͼȤˤʤޤ⤦ԤιҶϼޤ
423ʶ 11:31:08 36138
hide
äꥢ륿ǻäΤ

ǧڤ򤷤Ƥʤ
423ʶ 13:14:52 36139
R.K.
ѷä餷Ǥ͡
Фִִưޤ
425 11:16:00 36140
hide
Ǥ


k3ʾδȤȤ
5^k-1ޤ2*5^k-1ʿȤʤ褦k¸ߤ뤫

1֤ۤɹͤΤǤФޤ
⤷顢Фʤ⤷ޤ

ʤߤˤϤΤǤ


1/7=0.14 56224896
28112448
0.142857142857
Ȥ褦1/aa*b/10^(n+c),b/10^c̵¹¤Ȥɽ褦aƵ衣
(a,b,c,nϼ)1/7b=2,c=2,n=0ξ硣

1/2(b=2,c=1,n=0),1/3(b=1,c=1,n=0)ΤʬäΤǤ

ޤƬͤʤƤ򤱤Τʡ

52 14:27:54 36141
uchinyan
#36141
ͤƤߤΤǤʤʤ񤷤褦Ǥ
Τ褦ʤĤޤʤη󤬤ޤդʤȡa ϤǤ⤢ޤ͡

1/1 = (1 * 5)/10^(0 + 1) * (1 + 5/10^1 + (5/10^1)^2 + ...)
1/10 = (10 * 5)/10^(2 + 1) * (1 + 5/10^1 + (5/10^1)^2 + ...)
...
1/2 = (2 * 2)/10^(0 + 1) * (1 + 2/10^1 + (2/10^1)^2 + ...)
1/20 = (20 * 2)/10^(2 + 1) * (1 + 2/10^1 + (2/10^1)^2 + ...)
...
1/3 = (3 * 1)/10^(0 + 1) * (1 + 1/10^1 + (1/10^1)^2 + ...)
1/30 = (30 * 1)/10^(2 + 1) * (1 + 1/10^1 + (1/10^1)^2 + ...)
...
1/7 = (7 * 2)/10^(0 + 2) * (1 + 2/10^2 + (2/10^2)^2 + ...)
1/70 = (70 * 2)/10^(2 + 2) * (1 + 2/10^2 + (2/10^2)^2 + ...)
...

ʳˤ⡤Τ褦ʲ⤢褦Ǥ

1/5 = (5 * 8)/10^(2 + 1) * (1 + 8/10^1 + (8/10^1)^2 + ...)
1/55 = (55 * 32)/10^(2 + 3) * (1 + 32/10^3 + (32/10^3)^2 + ...)

ۤɤƱ褦ʷˤʤޤ

¾ˤ뤫ɤϡ褯ʬޤ (^^;
ͥνȡ 53ʷ 18:01:38 MAIL:uchi@sco.bekkoame.ne.jp 36142
⡼ޥ
#36142
uchinyan ^^
錄ͤƤǤ...
¤󼨤줿ηϤ褦ˡǸĤ줿ΤǤ礦...
...ˤΤĤ򤤤Ф꤬ΤǤ...~m(_ _)m~v
53ʷ 23:44:23 36143
hide
#36142
uchinyan
Ǥ͡郎­ʤޤ
عͧͤʹʤΤGWƤǤʤȳǧǤޤ
ȤꤢϤΤޤޤǹͤޤ
ȡnϼפǤϤʤ֣ޤϼפǤ

ʤߤˡʬ1ֶ᤯ͤ

̵¹¤
(10^n)/a=ca/(10^b-c)Ȥʤꤳ
a^2/10^n=(10^b)/c-1ѷ롣ġ
դʬm^210*m^21Ȥʤ롣mϼ
10*m^2ξ
դ10ܿˤʤˤϡʱաˡᣰȤʤʤФʤʤ
ΤȤm=0ȤʤΤŬ

c=10^b/2Ȥ뤳Ȥǡ롣
a^2=10^nȤʤ롣
a=10^p(pǤդ
m^2ξ
m^2=(10^b)/c-1
4Ǥξ;鱦դ2ΰ2İʾʤ
äơդ5^k-1ޤ2*5^k-1ѷǤkϼ
m^2=5^k-1ޤ2*5^k-1Ģ
(1)kΤȤ
Ԥ5^kʿȤʤΤ5^k-1ʿȤʤʤ
Ԥk=1Ĥޤa=7*10^pΤߤǤ뤳ȤǤ롣ʾϲ
(2)k=1ΤȤ
ơԤa=2*10^pԤa=3*10^pȤʤ롣
(3)k3ʾδΤȤ
???

ʾˡʤޤ꤭줤ʤɡġ
5^k=2r+1Ȥ
2(2r+1)^2-m^2=1Ȥʤ4Ǥξ;mϴʬ롣
m=2s+1
2r(r+1)=s(s+1)
Ȥʤr=2,s=3Ȥʤꡢk=1,m=7б롣
54ʲС 1:53:02 36144
uchinyan
#36144hide
䤽Ǥ͡郎­ʤޤ
ȡa Ф 10 Τ٤ǧʤСΤޤޤʤǤ͡
ȤꤢϤΤޤޤǹͤޤ
ϤǤȻפޤ
ʤβ򡤤Ȥ 10 Τ٤η󡤤⸫Ĥޤ
1/75 = (75 * 64)/10^(4 + 2) * (1 + 64/10^2 + (64/10^2)^2 + ...)

ʤߤˡʬ1ֶ᤯ͤ
ɤǤߤΤǤ褯ʬʤΤǶƤ

̵¹¤
(10^n)/a=ca/(10^b-c)Ȥʤꤳ
ȡb c ʸȿФȻפޤޤϤȤơ
a^2/10^n=(10^b)/c-1ѷ롣ġ
亸դʬm^210*m^21Ȥʤ롣mϼ
ʬʤǤa^2/10^n ȲꤷƤ褦˻פޤϤɤƤǤ
¿ʬȡ1/51/551/75 ϽФʤȻפޤ
䭡10*m^2ξ
䱦դ10ܿˤʤˤϡʱաˡᣰȤʤʤФʤʤ
䤷ΤȤm=0ȤʤΤŬ
OK
䭢1ʤ
c=10^b/2Ȥ뤳Ȥǡ롣
a^2=10^nȤʤ롣
a=10^p(pǤդ
OK.
䭣m^2ξ
m^2=(10^b)/c-1
4Ǥξ;鱦դ2ΰ2İʾʤ
äơդ5^k-1ޤ2*5^k-1ѷǤkϼ
ֱա->(10^b)/cפδְ㤤
m^2=5^k-1ޤ2*5^k-1Ģ
OK
(1)kΤȤ
Ԥ5^kʿȤʤΤ5^k-1ʿȤʤʤ
OK
Ԥk=1Ĥޤa=7*10^pΤߤǤ뤳ȤǤ롣ʾϲ
ϸǡ
(2)k=1ΤȤ
ơԤa=2*10^pԤa=3*10^pȤʤ롣
OK
(3)k3ʾδΤȤ
???
ϻޤʬʤǤϤʤǤ
ʾˡʤޤ꤭줤ʤɡġ
5^k=2r+1Ȥ
2(2r+1)^2-m^2=1Ȥʤ4Ǥξ;mϴʬ롣
OK
m=2s+1
2r(r+1)=s(s+1)
Ȥʤr=2,s=3Ȥʤꡢk=1,m=7б롣
¿ʬȤϻפޤʬʤǤ
ʤȤr=2,s=3װʳ˲򤬤ʤȤȼʤȾȤϤޤ
⤦ܺ٤ˤꤤפޤ
ͥνȡ 54ʲС 13:21:32 MAIL:uchi@sco.bekkoame.ne.jp 36145
uchinyan
#36143⡼ޥ󤵤
hide#36144ȴŪˤƱǤ򤱤Ƥޤ󤬡񤤤Ƥޤ͡

¤
1/a = ab/10^(n+c) * (1 + b/10^c + (b/10^c)^2 + ...) = ab/10^(n+c) * 1/(1 - b/10^c) = ab/(10^n * (10^c - b))
a^2 * b = 10^n * (10^c - b)
a^2 = 10^(n+c)/b - 10^n
a^210^n ϤȤ˼ʤΤ 10^(n+c)/b ⼫ǡmk 0 ʾȤơ
a^2 = 2^m * 5^k - 10^n
b = 2^(n+c-m) * 5^(n+c-k)
Ȥޤ¤ϡǽμǷޤ anmk Ф b ݤ c ˤϼͳ٤ΤǤ
b Ǿˤʤ褦 c ֤Ȥˤޤ
ǡޤ n = 0 ξͤƤߤޤ
ϡn = 0 ξβ
a^2 = 2^m * 5^k - 1
ĤСp 0 ʾȤơ
(a * 10^p)^2 = 2^(m+2p) * 5^(k+2p) - 10^(2p)
n = 2p ξβ⸫Ĥ뤫Ǥ
äϤñǤϤʤn Τʳβ⤢ޤϡ
b = 2^(n+c-m) * 5^(n+c-k)
m k n c ñȤ礭 n+c ʲξǤ
줬a = 5, 55, 75 ξǡϻԺǸĤޤޤ뤫⤷ޤ
n = 0 ξǤ
a^2 = 2^m * 5^k - 1
b = 2^(c-m) * 5^(c-k)
ξ c = max(m,k) ȤФǤ͡
ǡa^2 + 1 4 dzä 1 2 ;ʤΤ m = 0 1 Ǥǡ
(1) a^2 = 5^k - 1 ξ
m = 0, k = 0, a = 0Բ
m = 0, k = 1, a = 2, c = 1, b = 2
ϡʬޤ
ޤk 2 ʾζξ˲򤬤ʤΤ餫Ǥ礦
ϤʳǡϤʤǤʬäƤޤ
(2) a^2 = 2 * 5^k - 1 ξ
m = 1, k = 0, a = 1, c = 1, b = 5
m = 1, k = 1, a = 3, c = 1, b = 1
m = 1, k = 2, a = 7, c = 2, b = 2
ϡʬޤϡʳǤ
hideκǸʬξܺ٤˼Сk ξϲ褵ޤ͡

Ȥ櫓ǡǻ䤬ʬʤΤϡ
a^2 = 5^k - 1k 3 ʾδ
a^2 = 2 * 5^k - 1k 3 ʾ
n 1 ʾ n = 0 Ƴʤ
ˤʤޤ
ʤǽĤϡڥ
http://ja.wikipedia.org/wiki/%E3%83%9A%E3%83%AB%E6%96%B9%E7%A8%8B%E5%BC%8F
Ȥͭ̾η򤷤ƤΤǡ餫ΥץǤǤʵ⤹ΤǤ
ͥνȡ 54ʲС 13:27:33 MAIL:uchi@sco.bekkoame.ne.jp 36146
⡼ޥ
#36146
uchinyan ^^
ܺ٤ʲ⤢꤬Ȥޤ m(_ _)mv
ؤ᤿Ȼפޤ...^^;v

5^k-1=n^2 ...¸ߤ뤫ɤͤƤߤޤ...Ĥʤ饢ХȤǤ...^^;

5^k-1=n^2 Ȥ...
5-1=2^2 ʤΤ...

5^k-5=n^2-4=(n+2)(n-2)
5(5^(k-1)-1)=5*(5^((k-1)/2)-1)(5^((k-1)/2)+1)
n+2=5m
n-2=m+2
4=4m-2
m=3/2...ˤʤʤ...Τ̷
ǤϤᤫʤ...^^;?
54ʲС 13:51:45 36147
⡼ޥ
#36147
Ǥ...^^; Orz...
n+2=5m
n-2=m+4

m=2
n=8
5^k-1=8^2
5^k=65 ΤϤʤ...
ˤʤꤽ...?

ʬΤ꤬...°פ뤫ʤ...^^;?
54ʲС 13:59:54 36148
uchinyan
#36147#36148
5^k-5=n^2-4=(n+2)(n-2)
5(5^(k-1)-1)=5*(5^((k-1)/2)-1)(5^((k-1)/2)+1)
ǡm = 5^((k-1)/2) - 1 ȤƤΤǤ礦
ʤС
n+2=5m
n-2=m+2
βǽ⤢ޤ̤ˤ m ǿǤϤʤΤ m ǰʬ򤷤͡βǽꡤǤԽʬǤ
ʤ
n+2=5m
n-2=m+4
ϤषΤǤϡ
ͥνȡ 54ʲС 15:24:53 MAIL:uchi@sco.bekkoame.ne.jp 36149
⡼ޥ
#36149
uchinyan ^^
ޤäíܤˤʤäƤޤäƤޤ...^^;;; Orz...
n+2 n-2 Ϻ 4 ʤΤ...
...5, (5^(k-1)/2)1 ϸߤǤʤΤ...
n+2 or n-2 5 ǰȤƻ...
κ...Ǥ 5>4 κޤΤ...̷⤹...
ȸʤʤ...^^;?
54ʲС 15:59:16 36150
uchinyan
#36150
n+2 n-2 Ϻ 4 ʤΤ...
OK
䤷...5, (5^(k-1)/2)1 ϸߤǤʤΤ...
5 5^((k-1)/2) + 15 5^((k-1)/2) - 1ϡ줾ߤǤǤ͡
n+2 or n-2 5 ǰȤƻ...
OK5 ΰϤɤ餫Ƥޤ͡
䤽κ...Ǥ 5>4 κޤΤ...̷⤹...
ϡξȤ 5 ܿʤФޤǤϤʤΤǡ̤ˤϡޤǤβǤ̵ʵޤ
¾ξ򤦤ޤȤФΤΤޤ󤬡
ͥνȡ 54ʲС 18:03:53 MAIL:uchi@sco.bekkoame.ne.jp 36151
⡼ޥ
#36151
uchinyan ^^
ạ̈Ǥޤ...Orz
...Ǥ...^^;

5,m,m-2
Ǿξ...5,3,1
...5*1-3=2
ʾ...{(6,4)ʾ)ˤʤΤ...
5*(2m)-2g=4
ˤʤ(Ȥ...ηʤ)Ȥ...
g=5m-2
5*2m*2*(5m-2) =(n+2)(n-2) ʤΤ...
10m 2(5m-2) Ƥ!!......^^;?...櫓狼ʤȤȤäƤ뤫ʤ...

ΤȤ
10m*(10m-4)=5^k-5
4m(5m-1)=5^(k-1)-1
20m^2-4m+1=5^(k-1)

m=5g-1
20(5g-1)^2-4(5g-1)+1=4(5g-1)^2-4g+1=5-4g
g=5h
m=25h-1
20(25h-1)^2-4(25h-1)+1=20(25^2*h^2-50h+1)-4*25h+5
=25(20*25h^2-44h+1)
=5^(k-1)

20*25*h^2-44h+1=5^(k-3)
h=5a-1
20*25(5a-1)^2-44(5a-1)+1=100(5a-1)^2-44a+9
a=5b-4
100(5(5b-4)-1)^2-44(5b-4)+9=20(25b-21)^2-44b+37
b=5c+3

k-1 ͭ¤...0ˤʤ...
η׻̵¤³(줬ФǤ礦 ^^;)Τ...ʤäƤʴˤʤΤ...?

߻/...Orz...^^;v
54ʲС 19:52:11 36152
hide
#36145
uchinyan

2r(r+1)=s(s+1)
Ȥʤr=2,s=3Ȥʤꡢk=1,m=7б롣
¿ʬȤϻפޤʬʤǤ
侯ʤȤr=2,s=3װʳ˲򤬤ʤȤȼʤȾȤϤޤ
⤦ܺ٤ˤꤤפޤ

äȡǤϾˤʤäƤʤ⤷ޤ󤬡Τ褦˹ͤޤ
Ϣ³2Ѥ
2,6,12,20,30
Ȥʤ6,12)ȰʹߤȺ2ܰʾˤʤʤ
äƾΤϤΤߤǤȸ롣
ǤΤʤä԰¡

a^2/10^n=(10^b)/c-1ѷ롣ġ
亸դʬm^210*m^21Ȥʤ롣mϼ
䤳ʬʤǤa^2/10^n ȲꤷƤ褦˻פޤϤɤƤǤ
¿ʬȡ1/51/551/75 ϽФʤȻפޤ

äƤޤä
ä괪㤤Ƥ
ƻ1/5̵櫓

μʤͤuchinyan
a^2 = 2^m * 5^k - 10^n
b = 2^(n+c-m) * 5^(n+c-k)
μǹͤۤɤ
55ʿ 10:34:14 36153
uchinyan
#36153
2r(r+1)=s(s+1)
Ȥʤr=2,s=3Ȥʤꡢk=1,m=7б롣
¿ʬȤϻפޤʬʤǤ
侯ʤȤr=2,s=3װʳ˲򤬤ʤȤȼʤȾȤϤޤ
⤦ܺ٤ˤꤤפޤ

䤨äȡǤϾˤʤäƤʤ⤷ޤ󤬡Τ褦˹ͤޤ
Ϣ³2Ѥ
2,6,12,20,30
Ȥʤ6,12)ȰʹߤȺ2ܰʾˤʤʤ
r, s ٤礦ȤΤǤ礦
ȤǤʤȤñˤϡˤʤޤ
ʤȤȡr = 14, s = 20 ʤɤβ򤬤ޤ(¤̵ˤޤ)
2 * 14 * (14 + 1) = 420 = 20 * (20 + 1)
5^k = 2 * 14 + 1 = 29 k ¸ߤʤΤǡϸμβˤϤʤäƤޤ
ˤ衤ȤƤԽʬʵΤǡƹͤʤä褦˻פޤ

ԤͤäƤޤäΤǡ괺ץȤĴ٤Ƥߤޤ
δǤϡʤȤ n = 0 Ǥϡ¾˲ϤʤäȤƤ⤫ʤ礭 a ˤʤꤽǤ
n >= 1 ξ⡤ΤȤޤǰʳβϸĤäƤޤ

ʤȤ⡤n = 0 ξϡǤʤΤʤ
ͥνȡ 55ʿ 13:25:05 MAIL:uchi@sco.bekkoame.ne.jp 36154
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餫˥ߥäƤΤǤääƤȻפäΤˡ⤦Ƥʾ

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55ʿ 13:29:40 36155