ޥ
ߥޥ轵轵äǡ֤Ȥˤߥ򤷤Ť餤פȤȤˤޤץ񤤤Ƴǧޤ..

ŪʲˡꤷƤޤ־ʬפΤۤᤤ...ʰ̹ʤǤ
PowerBook 102ڡ 0:06:03 MAIL:masaru-y@sansu.org HomePage:Men @ Work32976
Taro
ȬΤγ̤Ϥ⤯ȤΤ褦Ȼפ2ޤ(^^;
ͽۤɤ5^5/3ˤƶᤤͤȤʤä褦Ǥ
102ڡ 0:06:41 32977
ߡ
33333ȴorz
102ڡ 0:08:39 32978

׻...
ӥ󥰤ζ 102ڡ 0:08:41 HomePage:32979
㡼ߡ
ɤ 1041 1042 ɤ餫ȤϤ˻פޤ
ܤΩƤƲ򤭤ޤ
Ȥ礦Ȥ䤯 102ڡ 0:08:50 MAIL:kakuromaster@star.cims.jp 32980
Ȥ
ᤴޤϥץǤǤޤ

FOR a=1 TO 8
IF a=2 OR a=4 OR a=6 THEN GOTO 50
FOR b=1 TO 8
IF b=2 OR b=4 OR b=6 THEN GOTO 40
FOR c=1 TO 8
IF c=2 OR c=4 OR c=6 THEN GOTO 30
FOR d=1 TO 8
IF d=2 OR d=4 OR d=6 THEN GOTO 20
FOR e=1 TO 8
IF e=2 OR e=4 OR e=6 THEN GOTO 10
LET x=a*10^4+b*10^3+c*10^2+d*10+e
IF MOD(x,3)=0 THEN PRINT a;b;c;d;e
10 NEXT e
20 NEXT d
30 NEXT c
40 NEXT b
50 NEXT a
END

󤵤1041̤ꡦ()
˭ԡ 102ڡ 0:13:43 MAIL:fttnm528@ybb.ne.jp 32981
ߡ
#32988ƱǤ͡

ʬѡ
¡äȤ
££ä¤ؤ3016480
£ããä¤ؤ20ߣ80
ãä¤ؤ10ߣ80
£££ãä¤ؤ10ߣ80
¤¤ؤģ32160
££££¤ؤģ32160
ס1040
ġ

ããããä¤ؤģߣᣱ
1041

䤤䡢ܤȤΤǤ
102ڡ 0:18:35 32982

3dzäޤܤ롣
;03;117;258Ȥ狼롣
53ܿˤʤȸȤϡ5ο¤3ܿǤ뤳ȤĤޤꡢ;ιפ3ܿǤ롣
Τ褦ʾ;ιפϡ0369Ǥ롣
11Ĥξ򿵽ŤĴ٤Ƥʤ1Ѥ

1ȯǤƤӤäꡪ

102ڡ 0:23:32 32983
ʸ
äȤޤ;ʬ
0,1,2,1,2
0ΤȤ00000ǣ̤
3ΤȤ12000,111001Ǥ2ढ뤫

('A`)

(5^5-5)/3+1=1041ʤƤäݤ
ʤǤ
102ڡ 0:49:42 32984
ʸ
Ʊ5¤Фʤ¤ˤƤ1/3γΨǽиȤȤ
3ʿäƤΤʡ
ʤ

102ڡ 0:53:35 32985
ڤפɡ
եܥʥåŪ˲򤭤ޤ
䤹ˡΰ̤˿դäȤͤ򤹤
;꣰;꣰ˣ­;꣱ˣ­;ꣲˣ­
;꣱;꣰ˣ­;꣱ˣ­;ꣲˣ­
ȤȡɽΤ褦ˤʤޤ


;꣰
;꣱
;ꣲ
102ڡ 1:44:59 32986
Mr.ǥ
ɤϣdzä;ͤʤ櫓뤳Ȥˡ
äȳڤˡꤽǸĤʤ !
Good night !
102ڡ 1:52:26 32987
⡼ޥ
ä줿
1,3,5,7,8 = 1,2,3,4,5 ʤΤǡ(mod 3)
15 οǤǤ3ʬ1ȹͤޤ
5^5/3=3125/3=10412
̩ʤɡ^^;
102ڡ 2:37:37 32988
λȼ
줿
׻ߥ򤷤ޤ
äȤǤġ
٤ߤʤ
zerostar 102ڡ 3:03:53 32989
Ȥ
ϴĥޤ
102ڡ 7:40:11 32990
ϥ饮㡼ƥ
Ϥ褦ޤ

˴ñʥץǤ夲ϥץ
ȷƤޤ
102ڡ 7:58:11 HomePage:湩ؤ˥32991
abcba@jugglermoka
3dzäƣ;ȣ;ƱǤȻפ
n:odd :(5^n)+13-1
n:even:(5^n)-13+1
ȤʤäΤǡn=5λˤʤȵޤ
102ڡ 8:18:34 32992

5ο5*5*5*5*5=3125̤ꡢ3dz1041;23dzڤ10411042Τɤ餫Ǥ뤬򾮤¤٤Ȥ־11111礭ʿ88888ϤȤ3dzڤʤΤ1041̤ꡣ
102ڡ 10:15:24 MAIL:y-ishino@nifty.com 32993
⡼ޥ
#32988 ɲ...
6ˡǡʤ1111155555 = 5^5 ޤǡ1ƹԤ顢
ǽ餬52
(2-0-1-2-0)-1-(2-0-1-2-0)-1-
Ĥޤꡢ
251
5^5/6=5202
Ĥޤꡢ2-0-1-2-0-1 520ġĤꡢ2-0 1Ĥǡ
2*520+1=1401
Ǹ夬1Ǥʤ0ȤΤ祤ʤ...^^;?
ɤ
102ڡ 11:29:59 32994
uchinyan
Ϥˤϡơϡ
οϡդǤʤȤ¿Ǥ
⡤5 Υɤ̤ΤʡȤѤʤȤͤƶ줷ߤޤ (^^;
ɡ̤ƻˤäƤǤޤ

5 3 ܿɤϳƷο¤ 3 ܿɤĴ٤ФǤ
ǡƷοϡ1, 3, 5, 7, 8 3 dzä;ܤޤ
1 -> 1, 3 -> 0, 5 -> 2, 7 -> 1, 8 -> 2 ǡ0, 1, 2 νиѥͤƤ줬 3 ܿˤʤõޤ
οϡ0 ʤ 3 1 ܡ1 ʤ 1, 7 2 ܡ2 ʤ 5, 8 2 ܤɬפޤ
0 5 Ĵޤ
3 ܿΥѥ 00000 ǡ¤ͤơ1 * 1^5 = 1 ̤ꡣ
0 4 Ĵޤ
3 ܿΥѥϤޤ󡣤ǡ0 ̤ꡣ
0 3 Ĵޤ
3 ܿΥѥ 00012 ǡ¤ͤơ5!/3!1!1! * 1^3 * 2 * 2 = 80 ̤ꡣ
0 2 Ĵޤ
3 ܿΥѥ 00111, 00222 ǡ¤ͤơ5!/2!3! * 1^2 * 2^3 * 2 = 160 ̤ꡣ
0 1 Ĵޤ
3 ܿΥѥ 01122 ǡ¤ͤơ5!/1!2!2! * 1^1 * 2^2 * 2^2 = 480 ̤ꡣ
0 0 Ĵޤ
3 ܿΥѥ 11112, 12222 ǡ¤ͤơ5!/1!4! * 2^4 * 2 * 2 = 320 ̤ꡣ
ʾǤ٤ƤǤǡοϡ
1 + 0 + 80 + 160 + 480 + 320 = 1041 ̤
ˤʤޤ
ͥνȡ 102ڡ 12:21:42 MAIL:uchi@sco.bekkoame.ne.jp 32995
uchinyan
ǼĤɤߤޤʬϰϤǡ

#32976#32977#32980#32986
äݤˡ

#32981#32991
ץˤˡ

#32982#32983#32984#32987#32995
ʬ 3 ܿƻ˿ˡ

#32988#32993
3 dzä;꤬ 0, 1, 2 θĿƱ餤ȹͤơ5^5/3 = 1041 ... 2 顤1041 䤹ˡ

#32994
6 ˡѡ
6 ˡǡ 5 2 Ȥ褯ʬʤ5 2 10 ˡ mod 3 ǤϤʤΤʡ
6 ˡ 11111 3 dzä; 1 Ǥä 2 ǤϤʤΤǤ
(2-0-1-2-0)-1-(2-0-1-2-0)-1-褯ʬʤ
11111, 11112, 11113, 11114, 11115, 11121, 11122, 11123, 11124, 11125, 11131, 11132, ... 顤
2-0-1-2-0 -0-1-2-0-1- 1-2-0-1-2- ...
Ǥϡ

#32992


ΤǤ#32986ܤǤ
˽äƤȤäƤޤ礦⹻ؤǤ

n ξ硤3 dzä;꤬ k θĿ a(n,k) Ȥȡ#32986ή˹ͤơ
a(n,0) = a(n-1,0) + a(n-1,1) * 2 + a(n-1,2) * 2
a(n,1) = a(n-1,0) * 2 + a(n-1,1) + a(n-1,2) * 2
a(n,2) = a(n-1,0) * 2 + a(n-1,1) * 2 + a(n-1,2)
a(1,0) = 1, a(1,1) = 2, a(1,2) = 2
Ǥǡ
a(n,1) - a(n,2) = a(n-1,2) - a(n-1,1) = (-1) * (a(n-1,1) - a(n-1,2)) = ... = (-1)^(n-1) * (a(1,1) - a(1,2))
= (-1)^(n-1) * (2 - 2) = 0
Ĥޤꡤ
a(n,1) = a(n,2)
ޤ
a(n,0) - a(n,1) = a(n-1,1) - a(n-1,0) = (-1) * (a(n-1,0) - a(n-1,1)) = ... = (-1)^(n-1) * (a(1,0) - a(1,1))
= (-1)^n * (1 - 2) = (-1)^n
ˡ
a(n,0) + a(n,1) + a(n,2) = 5 * (a(n-1,0) + a(n-1,1) + a(n-1,2)) = ... = 5^(n-1) * (a(1,0) + a(1,1) + a(1,2))
= 5^(n-1) * (1 + 2 + 2) = 5^n
ꡤǸμϡ
a(n,0) + 2 * (a(n,0) - (-1)^n) = 5^n
3 * a(n,0) = 5^n + 2 * (-1)^n
a(n,0) = (5^n + 2 * (-1)^n)/3

a(n,1) = (5^n - (-1)^n)/3
a(n,2) = (5^n - (-1)^n)/3
⤤ޤʤn = 5 Ȥȡ
a(5.0) = (5^5 + 2 * (-1)^5)/3 = (3125 - 2)/3 = 3123/3 = 1041
a(5,1) = (5^5 - (-1)^5)/3 = (3125 + 1)/3 = 3126/3 = 1042
a(5,2) = (5^5 - (-1)^5)/3 = (3125 + 1)/3 = 3126/3 = 1042
ˤʤޤ͡
ȡ#32992
n:odd :(5^n)+13-1
n:even:(5^n)-13+1
ϡa(n,0)
n:odd :{(5^n)+1}3-1
n:even:{(5^n)-1}3+1
ΤȤȻפޤ褦Ǥ͡
ͥνȡ 102ڡ 18:23:32 MAIL:uchi@sco.bekkoame.ne.jp 32996
Τޤ
Mr.ǥޡ
³Ԥ65Ԥˤ̾ޤ
ޤ(äˡ£áãġᣴ褫ޤ֤ˡ)򤴶ʤǤ礦
ꤤޤ
102ڡ 18:32:38 32997
⡼ޥ
#32996 uchinyan
Ǥ...äѤꤤøä...^^;Orz...

ŦΤ褦ˡ(2-0-1-2-0)+1 ˡ(0-1-2-0-1)(1-2-0-1-2)(2-0-1-2-0) Ƚ۴ĤȤƤ⡢5^5/(5*3)=2085
(2-0-1-2-0)-(0-1-2-0-1)-(1-2-0-1-2) ޤǤˡ05ĤʤΤǡ
208 * 5 =1040
;5Ĥˤϡ(2-0-1-2-0) 2Ĥ뤫顢
1042 Ĥˤʤä㤦...^^;?
ɤ
102ڡ 18:40:31 32998
ϺĹܲ
5֤餤ޤ
9ξϡ1111511133
12ξϡ11118
15ξϡ11157,11337,13335,33333Ȥ߹碌
äȽ񤭾夲Ƥä顢ǤϳפФƤơ
ǧ10ʾְä
1031ޤǸĤơֺϻߤᡪפȻפäޤޤ1041Ǥää줿

ˤƤ⤳ʬñ̤Dz򤤤ƤޤͤʤƤӤäǤ򸫤ƹȴ

ϡϲĽǤιֱδ֤⡢5-6ּȤߤޤ衣10IJϳƤΤʤ

Ǥ⡢19Ϣ³
102ڡ 20:17:44 32999
ϺĹܲ
ȡ10ĽФƤޤ6֤ĤĤѤ߾夲ǰ˵ϿĤƤ
9ξ2̤ˡ12(1)15(5)18(3)217ˡ245ˡ27(7)30(5)33(4)36(2)39(1)줾ξ1,5,10,20,30,60,120̤꤬ΤǷ׻ƹ1041̤ꡣäꤷޤ
103ʶ 9:32:14 33000
uchinyan
#32998
ȡܤĴ٤ʬȻפޤñ˽۴ĤʤȻפޤ
ͥνȡ 103ʶ 10:50:17 MAIL:uchi@sco.bekkoame.ne.jp 33001
⡼ޥ
ΤʺϤʤ顦ȤǤ...^^;

1111155555 mod 3 ΰܤѤͤƤߤȡ
333330 ˸äơDZоΤѲƤȹͤΤǡ2-0-1-2-0--0--0-1-2-0-1 ȤʤäƤϤ
Ĥޤꡢξü顢3=1+2=2+1=0+0 ˤʤäƤΤǡ
(5^5-1)/6=5204
ϡ-2-0-1- ʤΤǡ2--2-0-1--1 ˤʤäƤϤ
ʤС(5^5-5)/3+1=1041
104ڡ 1:16:42 33002
Mr.ǥ
> Τޤ
#32997ηɬ˹ͤ餫ˡDz򤤤ϤʤΤǤɤ򤤤ΤפФʤ
⺣̾ƤǤԤˤ줺פޤʥҥȤˤȲǤʤ
äϳΤǤ

ҥȤˤ뤳Ȥ³ƼΤ褦˺ޤΤǤϤȻפޤ
(1) ãĤ,äؤ褦ˤȤΣĤΰܤä' Ȥ롣
(2) ã'˴ؤƢã'ޤ֤ȤΣŤȤޤʳѤ礭δط £ä
ĹˣŤޤ
(3) ˡ¤˴ؤƢ£Ťޤ֤ŤƤȤޤ
(4) £ä̤äʿҤţ,ƣĹ餻С޳ѷˤǤ
¿ѷǤǤ͡ʾǤƤޤ

Dz򤯤ˤϾ嵭Τ褦޳ѷгˤäƤǤ˷ӤĤΤǤϤȻפޤ
ͤˤʤ뤫ʬޤ󤬡괺񤭹Ǥߤޤ

104ڡ 10:04:36 33004
Τޤ
Mr.ǥޡ
ǫʤ򤤤ɤ⤢꤬Ȥޤ
ѻͤˤʤޤ
104ڡ 15:17:34 33005
Ѥ
ƤƻäǤޤǤ
3dzäȤ1ޤ1,7
3dzäȤ2ޤ5,8
Ǿʬޤ
֡ 105 1:36:29 HomePage:33006
banyanyan
ϣ٤λäǤ
mod ǡȤơ
¤ΤȤ
̤
¤ΤȤ
ʣߣˡߣߣߣ᣸̤
ߣߣߣ᣸̤
¤ΤȤ
ߣߣߣߣߣᣱ̤
ߡʣߣˡߣߣߣߣᣴ̤
ʣߣˡߣߣߣ᣸̤
¤ΤȤ
ߣߣߣߣߣᣱ̤
ܣܣܣܣܣܣᣱ̤
ƱǤ
ܡ 108ʿ 3:17:38 HomePage:뤤²ײݻ33007