¤鷺٥ȥʰ켡ΩˤDz򤭤ޤorz
Ȥ鵤ŤޤǤޤǤ͡
褽140٤餤 315ڡ 0:06:21 29544
banyanyan
äƤϤʤΤʤΤǤ⤦ٹͤľƤޤޤ
315ڡ 0:07:43 MAIL:banyanyanmi@yahoo.co.jp 29545
ҥǡ
Ƕ̤δ֤ǻ줬ʤΤǵפ֤˻äޤ
äݤΤȽʡ
ΤΤβȡ 315ڡ 0:10:12 29546
JUN
£ӡãӤơΨѤƸޤ
315ڡ 0:10:13 MAIL:jmrtk800@ybb.ne.jp 29547
banyanyan
äƤϤʤΤʤΤǤ⤦ٹͤľƤޤޤ
315ڡ 0:10:23 MAIL:banyanyanmi@yahoo.co.jp 29548
sugitakukun
BSCSǤ֤äڤäƥ٥ķޤ
ǡAPS򭢡BPS򭣤ȤäƤΤǤARS2.5/4ȤʤäơAPS=16櫡^^;

˥ͥ饦ȤͤƤޤꡢϤ޷϶Ǥ^^;
ܣ˻ԣӶ衡 315ڡ 0:10:54 MAIL:sugitakuunikun@msn.com HomePage:White Shadow29549
ʸ
Ϥ䤤(^^;
315ڡ 0:11:40 MAIL:kyorofumi@msn.com HomePage:ʸ29550
ȥȥ
٤ޤľ٤Τǵ𤬣ʬ٤졣
£ӡ40ãӡ30ꢤңӡᣵ
16ܣˡ2/51/6315
ʼ˸лԡ 315ڡ 0:14:48 29551
banyanyan
äƤϤʤΤʤΤǤ⤦ٹͤľƤޤޤ
315ڡ 0:18:18 MAIL:banyanyanmi@yahoo.co.jp 29552
doba
Ф̤£äʿơäȤθԤȤȡ
ҡңԤϣ
ȤϡУԤ򡢢УӤȢУԣӤȢԣӤʬ䤷ơ
Ȥޤ
ޤ֤äפǤϤޤ͡
#29551ΥȥȥΤΤ᤯äǤ
315ڡ 0:20:48 29553
ʸ
ִ֣ӡӣѤ褦ȤƤޤޤ

ӣ=40ꢤӣ=30ʤΤǢӣ=6
УҤϢ£ä2/3 * 1/6 =1/15ʤΤ
£=(16+6)*15=315
315ڡ 0:23:51 MAIL:kyorofumi@msn.com HomePage:ʸ29554
⡼ޥ
ϴñǤ͢
̤׻Ǥޤ
16/((2/5)^2*(5/12)*(16/21))=25*12*21/4*5=315
315ڡ 0:28:27 29555
⡼ޥ
#29541
dobaء

ͧͤβȤʤȤʾ夸ʤ^^ Orz

ͧͲ

x^2+x+1=py(x,y)Ĥ褦ǿp
ͭ¸ĤǤȲꤷΤ褦ǿΤp1,..,pnȤ롣
P=p1p2..pnȤ롣
P^2+P+1ϤɤpiܿǤʤ
P^2+P+1ǤդǰqȤ롣
꤫x^2+x+1=qy⤿ʤϤǤ뤬
ºݤˤ(x,y)=(P,(P^2+P+1)/q)ȤäƤ̷Ǥ롣
315ڡ 0:36:38 29556
ǥ
B,C̤PRʿơȾľAQȤθT,U Ȥȡ
AS:ST:TQ:QUᣲȤʤ
ABC169/2*5/2*7/4ˡ315Ȥޤ
ˤƤ⳧ᤵˤ϶ޤ
315ڡ 0:46:09 29557
doba
#29556
⡼ޥ󤵤

ܼŪˤϡΤͧͤβȡƱȻפޤ
̵¤ˤפΤˡŪǼˡηȤä
ˡηȤäΰ㤤ʤΤǡ
ˡǽ񤤤̤⾯ʤƤ줤Ǥ͡

ȯۤϡǿ̵¤ˤפξƱ褦ʤȤФʡäƤȤϤơ㤢ȤꤢݤƤäơȸߤǤʤΤǤФʡȡ̤ä顢ǤääƴǤ
315ڡ 0:51:53 29558
⡼ޥ
#29558
dobaء

ʤۤɡľȯۤǤ͢
p^2+p-1 Ǥޤ͡
315ڡ 8:16:41 29559

ӣ¤֡ӣä֡
ӣ£ѡ᭤ӣãѡ᭣Ȥ
ȤϡդѤȤäơ

Уҡ£áᣲߣߣᣱܣܭ

£áᣲߣࣲᣳ

⤷ϡߡʣ/ˡߡʣ/ˡᣳ

315ڡ 9:15:44 HomePage:29560
Ѥ
PS:SR=16:5ΤɬǤ
SBSC֤ȤפĤʤäΤ
ޤޤԤ­ޤ͡

ޤˤ±˹ԤĤǤ
ĴˤϵĤƤ
֡ 315ڡ 9:28:15 HomePage:ʥڡ29561
uchinyan
ϤˤϡǯȤȤ⤢¿˻ǡ­ʤ³ƤޤȤ (^^;
ơǤϴñǤפĤˡ򤤤Ĥ񤤤Ƥޤ

(ˡ1)Ǥޤ
S BS C 򤽤줾ӤޤAPS = 16 cm^2 դޤ
APBP = 23 ʤΤǡAPSABS = 25 ǡABS = 40 Ǥ
BQCQ = 43 ʤΤǡABSACS = 43 ǡACS = 30 Ǥ
ARCR = 15 ʤΤǡARSACS = 16 ǡARS = 5 Ǥ
ǡAPR = APS + ARS = 16 + 5 = 21 ˤʤꡤ
ABC = AB/AP * AC/AR * APR = 5/2 * 6/1 * 21 = 315 cm^2 ˤʤޤ

(ˡ2)濴ˤޤ
P BC ʿԤ AQAC Ȥθ TU Ȥޤ餫ˡPTTU = 43 Ǥ
APPB = 23 = AUUC ʤΤǡAC 30 ȤߤʤȡARRUUC = 5718 Ǥ
T PR ʿԤ AC Ȥθ V ȤȡRVVU = 43 ʤΤǡARRV = 54 = ASST Ǥ
ǡAPT = 9/5 * APSAPU = 7/4 * APTABC = 25/4 * APU ʤΤǡ
ABC = 25/4 * 7/4 * 9/5 * APS = 25/4 * 7/4 * 9/5 * 16 = 315 cm^2 ˤʤޤ

(ˡ3)ͥ饦ȤäƤߤޤ
R BC ʿԤ APAQ Ȥθ DE Ȥޤ餫ˡDEER = 43 Ǥ
ARRC = 15 = ADDB ʤΤǡAB 30 ȤߤʤȡADDPPB = 5718 Ǥ
DPR ˥ͥ饦ȤȡPS/SR * RE/ED * DA/AP = 1 PS/SR * 3/4 * 5/12 = 1 PSSR = 165 Ǥ
ǡAPS = 16 cm^2 ʤΤǡ
APR = 21/16 * APS = 21/16 * 16 = 21
ABC = AB/AP * AC/AR * APR = 5/2 * 6/1 * 21 = 315 cm^2 ˤʤޤ

(ˡ4)ǽ餫ͥ饦ȤäƤߤޤ
P C ӡAQ Ȥθ X Ȥޤ
PBC ˥ͥ饦ȤȡPX/XC * CQ/QB * BA/AP = 1 PX/XC * 3/4 * 5/2 = 1 PX/XC = 8/15 Ǥ
PCR ˥ͥ饦ȤȡPS/SR * RA/AC * CX/XP = 1 PS/SR * 1/6 * 15/8 = 1 PS/SR = 16/5 Ǥ
ǡAPS = 16 cm^2 ʤΤǡ
APR = 21/16 * APS = 21/16 * 16 = 21
ABC = AB/AP * AC/AR * APR = 5/2 * 6/1 * 21 = 315 cm^2 ˤʤޤ

ޤޤʲˡꤽǤ͡
ͥνȡ 315ڡ 13:08:12 MAIL:uchi@sco.bekkoame.ne.jp 29562

ǼǤɤߤޤ

#29544
٥ȥ롣

#29547#29551#29554#29560#29565#29562(ˡ1)#29549
BSCS Ȥˡ

#29553#29562(ˡ2)
P ̤ BC ʿԤȤˡ

#29557, #29567
BC( Q)̤ PR ʿԤȤˡ
ϻפĤޤǤAQ ξ򽸤ư쵤˲򤯤ΤϡʤʤޤˡȻפޤ

#29555
ιͤܤƤʤΤǡŪˤʬ餺

#29562(ˡ3)(ˡ4)
ͥ饦ȤäβˡȤƤϡͥ饦ϤʤǤ礦͡
äȤ⡤䤬ͥ饦ΤäΤϻǤʤǤ(^^;

ʤˤϴطޤ󤬡⡼ޥ󤵤εɤߤޤ ^^
316ʶ 14:33:09 29563
ݤ
#29523
ǰǼ򡣺ϻäǤˤޤ
ޤεڤߤˤƤ޼
䤷Ƥ䤷Ƥä
315ڡ 14:27:21 MAIL:hopes@mba.ocn.ne.jp 29564
鿿
ޤޤ鿿ͤǤ
®Τۤ˻ޤäݤǤ
ޤդѤȤäAPS:BPSAP:PB23
ASB402ޤˡ§ȤȡSPB24cm2ˤʤޤ
ǡޤˡ§ȤäASB:ASC4340ᢢ302
ޤޤˡ§ȤäAR:ACASR:SRC151+5630cm2
ASR301/652äơPSSR165RB˸ޤȡPSBBSR165PSB24cm2BSR7.5cm2Ǥ
ơΤޤλˤäARB40+5+7.552.52
ޤޤޤˡ§ȤȡAR:RC15äΤ
52.5ߡ1+5ˡ315äơ31522Ǥʾ塡줿
ˡ3
315ڡ 18:06:39 MAIL:masa10223@yahoo.co.jp 29565
ʸ
Ф
316ʶ 0:34:39 29566

¡Ѥ̤УҤʿԤ
äȤθ򤽤줾ԡդȤ

ңԤʬˤʤΤǣԣä
򣴡ʬ뤫
ԣաᣲգáᣱ

ӡӣѡᣱܣᣲ

Ŭդ椬λȤä
֤˵ƤäƽФޤ

򸫤Ƥߤ
#29557
ǥΤȤۤƱͤǤ
316ʶ 1:59:52 HomePage:륯Υ֥29567
⡼ޥ
ʻפĤ

k,m pǿȤ

1+2+2^2++2^m=p^(2k+1)
1+p+p^2++p^(2k+1)=2^(m+1) ϡ

Ω뤫

ñʬޤͤ
礦ʤä餴ʤ^^;v

316ʶ 22:22:49 29568

#29568 ʤΤǤǤ
ǿϴʤΤǣᣲܣʣˤȤ
գܣ𡰣ܡģ𡰡ʣݣ
ᣲܣܡʣܣˡܡġʣܣˡʣݣ
ܴܡĴʣݣ
δĤ

դ϶դϴʤΤΤ¸ߤʤ
316ʶ 22:29:02 29572
⡼ޥ
#29568
󡢹ͤƲäƤ꤬Ȥޤ
ǽ󼨤Τ򾯤ѤľƤޤ
⤦٤ǧйǤOrz
+1 Τǡξդ϶ǤϤǤ^^;v
316ʶ 23:06:20 29573

#29568 狼ʤΤޤorz
316ʶ 23:40:56 29575
⡼ޥ
#29575
Orz
錄ʬʤΤǡˤҤͤäơ^^;
ʤȤϤ뤳ȤȻפäƤΤǤ
Ǥ⡢ɤ餫ΩĤΤʤǤ͡
317ڡ 8:46:39 29576
ǥ
#29568
ʻפĤ
k,m pǿȤ
1+2+2^2++2^m=p^(2k+1) .....(1)
1+p+p^2++p^(2k+1)=2^(m+1) ϡ......(2)
Ω뤫

Ǥk,m,pˤĤŪ˽񤫤ƤΤǡǤդ k,m (
),p(ǿ)ˤĤƤ뤫ȤȤˤʤޤ
3,k1,m2 ȤǤ⤪ȡ(1)(2)⤤ޤ
֤ΩʤפȤȤˤʤޤ
դϰ㤦ȤˤȻפΤǤĤޤ
㤨СǤդp(ǿ)ˤĤ(1)(2)ߤ褦k,mɬ
¸ߤޤפȤǤդp(ǿ),k()ˤĤ(1)(2)ߤ
褦mɬ¸ߤޤפȤʤΤ

δ㤤ʤ餴ʤ
317ڡ 9:10:19 29577
⡼ޥ
#29577
ǥء
Ŧ꤬ȤޤOrz
(1),(2) ƱΤĤǤ⤢뤫
ΰ̣ΤĤǤޤOrz

顢뤳Ȥ顢ꤵΤǤˡǾФϤʤǤ礦錄ˤʬʤΤǡͤΤϤ򤪼ڤǤФȡ^^;

(1)뤤(2) 褦ʤΤĤǤ⤢뤫
ˤʤΤʡ
ǤФ줷ΤǤ^^
317ڡ 12:07:04 29578
uchinyan
#29578#29577򤷤ޤԥޤ󤬡
k,m pǿȤ
1+2+2^2++2^m=p^(2k+1) .....(1)
1+p+p^2++p^(2k+1)=2^(m+1) ϡ......(2)
Ω뤫

(1),(2) ƱΤĤǤ⤢뤫
ʤС׻ơ
1 + 2 + 2^2 + + 2^m = (2^(m+1) - 1)/(2 - 1) = 2^(m+1) - 1 = p^(2k+1)
1 + p + p^2 + + p^(2k+1) = (p^(2k+2) - 1)/(p - 1) = 2^(m+1)
ǽμܤμơ
(2^(m+1) - 1) * p - 1 = 2^(m+1) * (p - 1)
p = 2^(m+1) - 1
ǽμȹ碌
p = p^(2k+1)
äơk = 0 ɬפǤk > 0 ʤΤǡ餫˥Ǥ͡

(1)뤤(2) 褦ʤΤĤǤ⤢뤫
ˤʤΤʡ
Ǥ
䤳ǤФ줷ΤǤ^^
ǥ󤬤ŦΤ褦ˡޤϡդΤˤ褵Ǥ

äɲ
⤽⡤
1 + 2 + 2^2 + + 2^m = (2^(m+1) - 1)/(2 - 1) = 2^(m+1) - 1 = p^(2k+1)
k, m, p ϡk > 0 ʤСʤǤk > 0 ʤС
2^(m+1) = p^(2k+1) + 1 = (p + 1) * (p^(2k) - p^(2k-1) + p^(2k-2) - ... + p^2 - p + 1)
ʤΤǡp >= 3 ꡤ
p + 1 = 2^n, 2 <= n < m+1
p = 2^n - 1
ǡ
2^(m+1) - 1 = p^(2k+1) = (2^n - 1)^(2k+1)
= (2^n)^(2k+1) - (2k+1)C1 * (2^n)^(2k) + ... - (2k+1)C(2k-1) * (2^n)^2 + (2k+1)C(2k) * 2^n - 1
2^(m+1) = (2^n)^(2k+1) - (2k+1)C1 * (2^n)^(2k) + ... - (2k+1)C(2k-1) * (2^n)^2 + (2k+1) * 2^n
2^(m+1-n) = (2^n)^(2k) - (2k+1)C1 * (2^n)^(2k-1) + ... - (2k+1)C(2k-1) * 2^n + (2k+1)
դ϶դϴʤΤǡϤꤨޤ
Ĥޤꡤk > 0 Ǥϡk, m, p ¸ߤޤ
¸ߤȤ顤
1 + p + p^2 + + p^(2k+1) = (p^(2k+2) - 1)/(p - 1) = 2^(m+1)
Ǥ͡
ʤk = 0 ʤС餫ˡm = 1, p = 3 Ȥơ
1 + 2 = 3
¸ߤޤޤΤȤ
1 + 3 = 4 = 2^2
Ǥ⤢ޤ
ͥνȡ 317ڡ 13:51:33 MAIL:uchi@sco.bekkoame.ne.jp 29579
doba
#29568ˤĤ

ܿͤν񤭹ߤˤꡢ
(1),(2)ƱΤĤǤ⤢뤫
Ȥ䤤ȤʤäƤޤ
ºݤˤϤäȶޤ
ǤΤϡʲƤǤ

̿꣱
1+2+2^2++2^m=p^(2k+1)褦
k,mȴǿpȤ¸ߤʤ

̿ꣲ
1+p+p^2++p^(2k+1)=2^(m+1)褦
k,mȴǿpȤ¸ߤʤ

̿꣱ŪäǤޤѷܹࡿʬ
̿ꣲˤĤƤϡǾʬɬפǤ
ξϸۤɡ

ʤߤˡ餫Ǥʤ֤ǤɤΤ褦ˡֻפġפΤ̣ΤȤǤ͡
317ڡ 13:33:02 29580
uchinyan
#29580
̿ꣲ
1+p+p^2++p^(2k+1)=2^(m+1)褦
k,mȴǿpȤ¸ߤʤ
դࡤ⤤ΤǤ

ʤߤˡ餫Ǥʤ֤ǤɤΤ褦ˡֻפġפΤ̣ΤȤǤ͡
Τ ^^
ͥνȡ 317ڡ 14:05:08 MAIL:uchi@sco.bekkoame.ne.jp 29581
⡼ޥ
#29579,#29580,#29581
uchinyandoba󡢤꤬Ȥޤdoba󡢥ǥ󡢼餷ޤ^^;)

ǤǤ͡

ɤƻפĤȤȡ
δʤǤ

¤ϡ(1+1/p+1/p^2++p^n_1)*(1+1/q+1/q^2++1/q^n_2)*ʤΤǡ
((1+p+p^2++p^n_1)/p^n_1)*((1+q+q^2++q^n_2)/q^n_2)*
Ȥʤޤ͡
δϡ2˻ĤΤǡ((1+2+2^2++2^n_1)/2^n_1) ͤˡ((1+p+p^2++p^n_2)/p^n_2) ݤƤѤ2ˤʤ櫓Ǥδϡ2^(m+1)-1 ǿλˡ2^m*(2^(m+1)-1)Ȥ˸¤뤳ȤƤΤǡ
ȤƤϡ2^m,2^(m+1)-1 ǤꡢΤȤ
((1+2+2^2++2^m)/2^m)*(1+(2^(m+1)-1)/(2^(m+1)-1)=2 ȤˤʤޤǤ
Ĥޤꡢ¾ξ硢Фñʻ(p^(2k+1)/2^m)*(2^(m+1)/p^(2k+1)) 2ˤϤʤʤΤǡʬ¤ʬҤˤʤ褦ʤΤ줾ʤäȤƤ⡢ƱΤϤʤϤäƤȤ顢ˤǤ^^;
ͤȤơȤжƲޤOrz
317ڡ 20:38:27 29582
doba
̿꣱ˤĤƤ#26579ɲäνˤ褦ʤΤǡ̿ꣲ

k,mȴǿp
1+p+p^2++p^(2k+1)=2^(m+1)Ȳꤹȡ
ξդp-1򤫤
p^(2k+2)-1=(p-1)2^(m+1)

i) kΤȤ
k=2nnϼˤȤ
p^(2k+2)-1=p^(4n+2)-1
=(p^2-1)((p^2)^2n+(p^2)^(2n-1)++(p^2)+1)
=(p-1)(p+1)((p^2)^2n+(p^2)^(2n-1)++(p^2)+1)
ʤΤǡ
(p+1)((p^2)^2n+(p^2)^(2n-1)++(p^2)+1)=2^(m+1)
Ȥʤ롣
(p^2)^2n+(p^2)^(2n-1)++(p^2)+1ϴĤʤΤǡ
ǤʤǤꡢǿ˻ĤΤǡ̷⡣

ii) kΤȤ
k=2n-1nϼˤȤ
p^(2k+2)-1=p^(4n)-1
=(p^(2n)+1)(p^(2n)-1)
=(p^(2n)+1)(p-1)(p^(2n-1)+p^(2n-2)++p+1)
ʤΤǡ
(p^(2n)+1)(p^(2n-1)+p^(2n-2)++p+1)=2^(m+1)
Ȥʤ롣
ǡp^21 (mod 4)ꡢp^(2n)+12 (mod 4)Ȥʤꡢ
(p^(2n)+1)/2ϣǤʤǤꡢǿ˻ĤΤǡ̷⡣

̷꤫⤬Ƴ줿ΤǡΤ褦ʤȤϵʤ
ʾ

ʤߤˡ̿꣱Ǥ
2^(m+1) = p^(2k+1) + 1 = (p + 1) * (p^(2k) - p^(2k-1) + p^(2k-2) - ... + p^2 - p + 1)
ˤơ(p^(2k) - p^(2k-1) + p^(2k-2) - ... + p^2 - p + 1)Ǥ꣱ǤʤȤ顢¨¤̷⤬Ƴޤ

#29582 ⡼ޥ󤵤
ʤۤɡǤ
317ڡ 17:38:09 29583
uchinyan
#29583
ʤۤɡΤˡ
äˡ̿꣱λξʬ̵̤ޤ (^^;
Ŧ꤬Ȥޤ
ͥνȡ 317ڡ 17:47:53 MAIL:uchi@sco.bekkoame.ne.jp 29584
ǥ
#29583
doba󡡸Ǥ͡
317ڡ 18:35:29 29585
⡼ޥ
#29583
dobaء
꤬ȤޤOrz
uchinyanȤͤȤʤƤȤ⤿䤹˲򤫤ΤǤ礦^^v
ʥҥȤפޤ^^vv
317ڡ 18:40:38 29586