ʤ
ɤǸǤ
http://micci.sansu.org/tokubetu/tokubetu-002.htm
̳ƻ 811ڡ 0:06:50 MAIL:naka@sansu.org HomePage:naka's Home Page25586
ޥ
ҤǤ𤷤ʤ..ߥΤǤȤꤢ˸ޤm(__)m
PowerBook G4 811ڡ 0:07:21 MAIL:masaru-y@sansu.org HomePage:25587
ߥƥ
2,2,3 6,10,15 Σ̤ɤäǤ礦
811ڡ 0:07:24 25588
Ϥʤ
a,b,cȤȤ
ʤȤb=2a-2Ǥ

줬狼äƤa=9,8,7,5,4,äƤᤷ6ǤäȤߤĤäʾ
811ڡ 0:08:53 25589
ޥ
ѤߤäȤ...

֣פ곰ǤʣΤĤäΤ...ˤޤä...
PowerBook G4 811ڡ 0:09:21 MAIL:masaru-y@sansu.org HomePage:25590
ޥ
֣פɲäޤȤ櫓ǡ𤷤ޤ...m(__)m
PowerBook G4 811ڡ 0:10:43 MAIL:masaru-y@sansu.org HomePage:25591
ߥƥ
֤󡢤٤ưۤʤȴΤǡ
6,10,15 ˲ޤ
񤤤ƤͤϾʤȻפޤ(^^;;
811ڡ 0:10:43 HomePage:ߤ25592
taku
ʤȤʤexcelN,N+4,sum(n;n+4)-1n=6 ΤȤȤ߹碌
6,10,15 äǤ
811ڡ 0:13:07 MAIL:takuo@kcv.ne.jp 25593
Gou
󡢵פ֤Υꥢ륿໲á
ƻõޤ
ۤ¡äȤȤ
֤󡢣áܣܣ¡Ŭ˲ꤷơ

ǯ٤СӤʤ
811ڡ 0:16:08 25594
Ϥʤ
a2a-2,3a-3ηʤΤ

ȡa=2,3,6Ωʤ
811ڡ 0:16:51 25595
Ȥ
ͤ˽basicǰʲ
for a=1 to 100
for b=1 to 100
for c=1 to 100
let x=a+b
let y=a+c
let z=b+c
IF MOD(x,c)=1 AND MOD(y,b)=1 AND MOD(z,a)=1 THEN PRINT a;b;c
next c
next b
next a
END
2 2 3
3 4 6
6 10 15
ǤƤƤĤ̤褫äƤ褫äǤϡ
˭ԡ 811ڡ 0:17:28 MAIL:fttnm528@ybb.ne.jp 25596
ߤ
2,2,31ĤʤǤͤ͡abcǹͤƤޤΤǡ
դĤ6,10,15פĤޤǤ
ߤɡ 811ڡ 0:23:17 25597
tomh

١ⶶΤȤDz򤤤ä (^^;
ԡ 811ڡ 0:35:26 MAIL:tomh@yahoo.co.jp HomePage:H to M25598
manabu
ɤ礭ʿȤäƤϣĤʤǤ͡
ʤʤȻפޤ
811ڡ 1:42:50 25599
manabu
ɤ礭ʿȤäƤϣĤʤǤ͡
ʤʤȻפޤ
811ڡ 1:43:28 25600
ҡΤ
Ȥꤢa+b+cadzäƤbdzäƤcdzäƤ1;󤸤ʤȸȤ
餷ߤĤ֤Ǥʡ
2,2,3ȯޤ
9ߤ濴 811ڡ 3:07:47 HomePage:25601

ĤʤȤˤ餤֤äʰʲά

ޤ뻰a,b,cȤ
b+c=(p-1)a+1 , c+a=(q-1)b , a+b=(r-1)c+1
Ȥ롣p,q,r>1
ĥäƷ׻pqr+k=pq+qr+rpk)Ȥʤꡢp,q,rΤǾΤΤ2ʤΤr=2Ȥ,(p-2)(q-2)=3-k
äƤϤޤk0,1,2λʤΤǾa,b,cȤϻ

ñˡΤꤿ
̤̪ 811ڡ 3:07:48 MAIL:ishizaki@qa.so-net.ne.jp 25602

ˤʤäƴñʲפĤäơ

a+b=pc+1 , b+c=qa+1 , c+a=rb+1Ȥ2(a+b+c)=pa+qb+rc+3
pqrȤ(p,q,r)=(1,2,k)k2ˤͭʤȤʬ롣
ȤϸμƤϤƲ򤯤,k=2,3,4λ
̤̪ 811ڡ 3:39:54 MAIL:ishizaki@qa.so-net.ne.jp 25603
㡼ߡ
äƤ뤳ȤƱǤ3Ĥμεտ¡פԥȤޤ

a+b+c-1=NȤȡNa,b,cܿN=pa=qb=rcȤ롣
1/p+1/q+1/r=a/N+b/N+c/N=(N+1)/N>1.
pqrȤȡp,q,rȤ
(1,q,r),(2,2,r),(2,3,3),(2,3,4),(2,3,5)Τ(ưפʤΤά)
1ܤN=aŬ2ܤc=1Ŭ
Ȥ3Ĥ餽줾(a,b,c)=(3,2,2),(6,4,3),(15,10,6)롣
811ڡ 4:09:44 MAIL:ojamaru@amber.plala.or.jp 25604

10ǯʾؤǽꤵƤǤȻפޤ
811ڡ 7:32:15 25605
ޥ
Ϥ褦ޤϲƴֽ٤ߤȤΤˡʤȤ˸¤äƼܤƤޤޤ(^^;;

ȡĤʤ2,2,3곰Ǥ..ˤȤϤƤǤˡ#25603ΤˡƱǤϤɤǸΤʤΤǤʼ¤Ϥ졢ǯʾ˥ܥĤˤǡȷ̤ν񤤤ѤʸեĤäƤǤˡ#25605ι椵Τä餹ȡβ򸫤ΤΤޤ...
ʤߤˡ֣ĤϣοפȤϹꥮɲäޤDz򤯤ȤʤȤɤƤֻԺפäƤȤˤˤʤޤ...

ʤߤ˺󡢹ʬ餤ޤǤ̤ǤϤޤˤνͤƤޤɤƤȤʤơöܥĤˤޤޤޤɤäܤ򸫤...Τޤ󤷡¢꤫Τޤ...ʷ빽˺ƤޤΤǡ
PowerBook G4 811ڡ 7:55:59 MAIL:masaru-y@sansu.org HomePage:25606
ޥ
ΤΤ餻
ȡ8/26ʶˤYokoyaMacʤ¸ʤ¿ˤˤä뤳ȤˤʤäƤޤȤ櫓ǡݤ߲򳫺ŤפäƤޤΤǡäϻޤǥᥤĺйǤʤߤ˾ϽëޤդǡͼȾȤΥȤˤʤ뤫Ȼפޤ
PowerBook G4 811ڡ 7:57:58 MAIL:masaru-y@sansu.org HomePage:25607
nakakun
ֻǤȤʤȤˡˤʤΤǤ礦դꣳĤο¤ϣĤοθܿץ饹ˤʤΤǡĤοۤʤϡܿ򣱤Ȥȡ1/21/31/4(6+4+3)/12=13/12ꡢʣˡ1/2+1/3+1/5=(15+10+6)/30=31/30ꡢʣˡΣȤ狼롣ʤߤˡƱäƤ褤ϡ1/2+1/3+1/3=(3,2,2)/6=7/6ꡢʣˤΩĤȤ狼ޤ
ܡ 811ڡ 9:04:28 25608
DrK
ϤñƤϤޤ
礭ʿȡ¾2Ĥο¤Ȥκ1ȤȤϤޤ
ȡ2ܤοФƤ¾2Ĥο¤2ܤ1礭ʾǤʤФʤʤ
顢(6,10,15)
ϳڱफ?㤦ʡ 811ڡ 9:15:22 MAIL:satoka@star.odn.ne.jp 25609
kasama
Ϥ褦ޤȤʤ6,10,15٤פդޤ(^_^;
811ڡ 9:16:09 25610
DrK
#25607
YokoyaMacϺͤˤäΤǤϤʤΤǤԷΥ줿ΤǤ
ϳڱफ?㤦ʡ 811ڡ 9:16:31 MAIL:satoka@star.odn.ne.jp 25611
Toru Fukatsu
ȤۤƱȻפޤȤƤ򤫤äΤǽ񤭹Ǥߤʤޤabc Ȥȡa+b=pc+1, a+b2cp=1a+b=c+1a+c=qb+1 cõơ2a=(q-1)b+2 ,ab q=1 or 2q=1 λa=1Ǥ뤬Ŭq=2λb=2a-2 ,c=3a-3 b+c=ra+1=5a-5 (5-r)a=6äơa62,3,6(a=1Ŭ)a=2 λb=2,c=3a=3λb=4,c=6 a=6λb=10,c=15դ
811ڡ 11:02:04 MAIL:tfukatsu@tth-japanpost.jp 25612
uchinyan
ϤϤ褦ޤ
ǽ鸫Ȥϡˤ⡢֥ץȤǤ͡ꤤפȤʤΤǡͶǤ˾ƤĤ(^^;
(2,2,3) (6,10,15) ĤФƤΤϡȤǤ礦äȤ⡢ԤϡԺǤ⤹˸Ĥޤ͡
θ塢ؤǤ줷ʤȤåޤϳƱ褦ʤΤǾάޤ
ǤϡĤο¤ǾܿβܡܣʤΤǡƥˤƻԺΤǤ礦
轵ϡƵ٤ߤǤϤʤΤǤ ^^/
ͥνȡ 811ڡ 11:21:16 MAIL:uchi@sco.bekkoame.ne.jp 25613
ϲ
ɤǸȤ褦ʡȻפä顤(^^;)ΣȣФä
http://www.geocities.jp/hagure874/math/m125.html

ԤʤΤǡä礷Ƥ
http://www.geocities.jp/hagure874/

811ڡ 11:29:39 25614
uchinyan
ǼĤɤߤޤ󡢴ŪˤϡϤꡢ
ήˡ¿Υ
Ĥ¤ܿܣ
ץ
Τ줫Τ褦Ǥ͡
ʤߤ˻οزˡϡToru Fukatsu Τ˰ֶᤫäǤ
ͥνȡ 811ڡ 11:45:25 MAIL:uchi@sco.bekkoame.ne.jp 25615
ϥ饮㡼ƥ
ץǤ

ܤΤߤǵʤޤǯϵ˽ߤޤ
̶彣 811ڡ 17:37:25 HomePage:ĩ25616
⡼ޥ
Ʊ褦Ǥ
a+b=c+1
a+c=nb+1
c-b=nb-c
2c=b(n+1)
2a+2b=2c+2=b(n+1)+2
2a=b(n-1)+2
n=2
2c=3b
2a=b+2
b+c=ma+1=b+3b/2=m(b+2)/2+1
2b+3b=m(b+2)+2
(5-m)b=2m+2
b=(2m+2)/(5-m)
m=3,b=4,c=6,a=3
m=4,b=10,c=15,a=6

ͧͤΡ
3Ĥμꡢɤ2ĤѤĤμdz
;꤬1Ȥʤ롣Τ褦ʼȤ衣
814 19:03:26 MAIL:kennji72001@yahoo.co.jp 25617
uchinyan
#25617
ͧͤΡ
3Ĥμꡢɤ2ĤѤĤμdz
;꤬1Ȥʤ롣Τ褦ʼȤ衣
2, 3, 5 ʡ
ϡƱ褦ˤ礳礳ФǤޤ͡
ͥνȡ 815ʷ 15:26:55 MAIL:uchi@sco.bekkoame.ne.jp 25618
⡼ޥ
ͧͤΡ
3Ĥμꡢɤ2ĤѤĤμdz
;꤬1Ȥʤ롣Τ褦ʼȤ衣

錄Ϥ򤭤ޤ
ab+bc+ca-1=nabc Ȥȡ
ab=nabc-c(a+b)+1 顢c dzȣ;ꡢ
ʲƱ͡
ξդabc dzȡ1/c+1/a+1/b-1/abc=n
a<b<c Ȥȡa ϣʾʤΤǡ3/2-1/8=11/8<2 顢
n=1
Ĥޤꡢ1/a+1/b+1/c-1/abc=1
ǡa ʾȱդϣʲˤʤΤǡa=2
1/2+1/b+1/c-1/2bc=1
2/b+2/c-1/bc=1
ǡb ʾȱդϣʲˤʤΤǡb=3
2/3+2/c-1/3c=1 顢2/c-1/3c=1/3
6-1=5=c
Ĥޤꡢ(a,b,c)=(2,3,5)
ιͤ餷ơƱλϤʤΤǡϤ
815ʷ 18:32:44 MAIL:kennji72001@yahoo.co.jp 25619
uchinyan
#25619
ɤƱǤξϡǽ顢
ab = rc+1, bc = pa+1, ca = qb+1
Ȥơ
(ab-1)(bc-1)(ca-1) = pqr * abc
abc * (abc - (a+b+c)) + (ab+bc+ca-1) = pqr * abc
ǡ
ab+bc+ca-1 = nabc
ȤơʲƱ (٤Ȥϰ㤦ɡ)
ȹͤޤ ^^;
ͥνȡ 816ʲС 11:59:20 MAIL:uchi@sco.bekkoame.ne.jp 25620
⡼ޥ
軲鵢ä顢ͧͤ餳꤬Ƥޤ
Ť˲򤱤Τĩ路ƤߤƲʤߤʤˤϴñ⡩

|a||b||c||d|1ΤȤ衣
a+b+c+d-abcd3
816ʲС 16:25:36 MAIL:kennji72001@yahoo.co.jp 25621
uchinyan
#25621
|a||b||c||d|1ΤȤ衣
a+b+c+d-abcd3
ޤ
a + b - ab - 1 = -(1-a)(1-b) < 0

a + b - ab < 1
ˡ
a + b + c - abc - 2 < ab + c - abc - 1 = -(1-ab)(1-c) < 0

a + b + c - abc < 2
ơ
a + b + c + d - abcd - 3 < abc + d - abcd - 1 = -(1-abc)(1-d) < 0

a + b + c + d - abcd < 3
Ʊͤˤơ̤ˡ
|a1|, |a2|, ..., |an| < 1 ΤȤ
a1 + a2 + ... + an - a1 * a2 * ... * an < n-1
Ǥ͡
ͥνȡ 816ʲС 21:38:45 MAIL:uchi@sco.bekkoame.ne.jp 25622
⡼ޥ
#25622:uchinyan 󡢤Ǥ̲͡ǤƤޤ͡
|a||b||c||d|1ΤȤ衣
a+b+c+d-abcd3
錄ϡ
a+b-ab<1
c+d-cd<1
a+b+c+d-ab-cd<2
ab+cd-abcd<1
ʾꡢ
a+b+c+d-abcd<3
ȤޤǤϹबλ̲Ǥޤͤ
816ʲС 23:32:40 MAIL:kennji72001@yahoo.co.jp 25623
ȥȥ
ϹǤ礦
ǯλϥޥ뤵󤬹ɤä褦ʡ
ʼ˸лԡ 817ʿ 23:18:04 MAIL:h-sakai@zb3.so-net.ne.jp 25624