Ȥ
1+7+43+49+25+4+22+46+28=225
˭ԡ 101ڡ 0:16:36 MAIL:fttnm528@ybb.ne.jp 43732
(Keigei)
ǧڤ150Ǥ
25ĤȤǤΤǡо
100ܿ25ɽˤʤꤨޤ͡
ºݤˤϡ줾ο򣳤dzä;񤭹ȡ
16,17,16Ǥ
ޣĹ֤С;꤬,,ΣĤ뤳Ȥˤʤꡢ
;꤬ν꤬;뤳Ȥˤʤޤ
оΤ֤ͤСоΤʰ֤;꤬νޤ
ºݤˤϡ,,,22,25,28,43,46,49 ǡΤĤޤΤǡ
¤ 225 Ǥ
101ڡ 7:44:12 43733
ޥ
ߤޤǧѤΥե뤬äȴְ㤨ޤޤǤ...餷ޤm(__)m
MacbookPro 101ڡ 12:21:00 43734
ǯ
Ϥ21Υ֥åǡֻĤäƤޤ1ޥֹϤĤפɤߴְ㤨ơ25äˡ֡ޤֹ¤Ƥפɤǡ625äǼĤ줺褯ɤ31Υ֥åäɡ225äơǰΤ31Υ֥åäƻԺ
25ϳǤꡢ¾ξ˳ս꤬Со100ܿǤ롣о25Ȥͤˤʤ뤳Ȥưפˤ狼롣2251225ޤǤǧڤꡣǤʤǼĤ줺
α߼Ψ3.14η⤢ꡢޥ뤵Τ鿴ȤȤǡɿƤޤä
101ڡ 12:54:23 43735
uchinyan
Ϥˤϡơϡ
ǽϡо鴪 1 + 4 + 7 + 22 + 25 + 28 + 43 + 46 + 49 = 225 ʡȻפǧڤ饢ȡ
ʴŤʤŪ˹ͤƤƱǤϤԷǼĤˤ줺
ٹͤľƤ 225 ʤΤǡȤä顤԰̾ܤޤ
ϤäԷǼĤˤơҤȤޤϤ褫äǤˡϤʴǡ

7 * 7 Υޥܤ 1 * 3 Ĺ֤Ȥ
Υޥܤο¤ϡĹĤˤƤⲣˤƤΥޥܤο 3 ܤǾ 3 ܿǤ
ǡĤ룱ޥʳο¤ 3 ܿǤ
ǡ7 * 7 Υޥܤο¤ϡ1 + 2 + 3 + + 49 = (49 * 50)/2 = 1225 = 408 * 3 + 1ʤΤǡ
ޥ 3 ܿˤʤɬפ뤳ȤꡤĤ룱ޥθ 3 dzä 1 ;뼡ˤʤޤ
1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49
ȤޤоꡤĹ֣ĤФơ
4 ΥޥܤνĤ22 Υޥܤβιԡ1 ΥޥܤμФ7 ΥޥܤμФ
Τ줾˴ؤоΤ֤ǽˤʤޤ
ǡ嵭λĤ룱ޥФơ㤨С4 ΥޥܤνĤоΤʼǽʤϤǤ
7, 4, 1, 12, 9, 20, 17, 28, 25, 22, 33, 30, 41, 38, 49, 46, 43
󤳤ۤɤ 3 ܿξʤФʤʤΤǡϡ
1, 4, 7, 22, 25, 28, 43, 46, 49
˹ʤޤƤ¾оξޤºݤ˼¸ǽʤΤưפʬޤ
ǡǽʻĤ룱ޥϡ1, 4, 7, 22, 25, 28, 43, 46, 49 9 ġǡ
= 1 + 4 + 7 + 22 + 25 + 28 + 43 + 46 + 49 = 50 * 4 + 25 = 225
ˤʤޤ
ͥνȡ 101ڡ 14:05:44 43736
uchinyan
ǼĤɤߤޤ
ԷǼĤؤǥȥ֥뤬äΤǽ񤭹ߤʤǤ͡
ΤȤϡĤ룱ޥ 3 dzä 1 ;ڤоȤˡΤ褦Ǥ

θ塤񤭹ߤΤǡ

#43732
̤ͿƤޤܺ٤

#43733#43736
Ĥ룱ޥ 3 dzä 1 ;ڤоȤˡ

#43735
о 100 ܿ + 25 ǧڡˤˡ

#43738
7 * 7 Υޥܤ(i,j)i, j 1 7 Ȥơ ij Τ줾¤
7 * 7 ΤǤϤȤ 3 dzä 1 ;Ĥ1ޥȤȤ 3 ܿ顤
Ĥ룱ޥ (i,j) ij ϤȤ 3 dzä 1 ;ˤʤ뤳Ȥ⤯ˡ
ϿؤˤʤäƤޤǻˤʤȻפޤ
#43733ʤɤоʬ (i,j) Ȥ̤ƤޤäƤȻפޤ

#43740#43749
оȻԺˤˡ

#43748
ץˤˡ
ͥνȡ 102ʶ 14:02:42 43737

Ūˤ¾Ʊǡ;ܡ
̵֤뤷ʻҤʣ顤ˤɽȡĤ­Ƥⲣ­Ƥ⡢ĺɸɸȤˣܿ

1+2+3+4+5+6+71(mod3)
71(mod3)ʤΤǡ
IJɸȤˡĤ
飹ĤγʻҤ˳Ƥ줿פƣ
101ڡ 15:27:54 43738
ܡʥ
Ʊ褦 7x7 ˡ15 Ĥ1x3 Ĺ 1 Ĥ 3 ΤߤͤȡɤʤǤ礦

ߤˡϡʲΤ褦ʷǤ




101ڡ 16:42:06 43739

ĤΤ褦ˤdzǧƤ褦ȣǽ졢Ⱦʾ夿äƤޤޤȥ֥äǤ͡
оηʤΤǡʣߣޥޤΤǡĤΡˣߣޥˣޥΥ֥åƤɤ˷֤Ǥ뤫ǹͤޤ
줷ʤȻפʤ顢äʤΤѤ餺μ夵Ǥ
̾Ƥޤ֥åưƱΥ֥åиƳѥʤäƤΤϡɱ͵߽Хפȸ̾ȳäˤפФޤ
101ڡ 18:38:43 43740

#43739ܡʥꤵꣴǤ礦
4ߣޥ13ޥġȡ4ޥϣˤäΤǡȿ¦ȥåȤǣȡоΤʤΤǣܤƣߣߣᣴ
101ڡ 19:14:42 43741
ǯ
#43733(Keigei)Ρ3dzä;ͤȤΤˤϡ֤ʤۤɡפȴޤ31Υɤ¤ε§ͤƤޤޥֹȴϢŤȤϻפĤޤǤ
ֺоΤ֤ͤСоΤʰ֤;꤬νޤ פιͤκ򤬤狼ʤΤǤƤʤǤ礦
κоΤȤȤʤ顢41оΤǤϤʤΤǤϡǺǤޤ

101ڡ 19:39:51 43742
(Keigei)
#43742 ǯԤ
dzä;񤭹
,,,,,,
,,,,,,
,,,,,,
,,,,,,
,,,,,,
,,,,,,
,,,,,,
ǡޣ16碌ȣĻĤޤ
դˤȡ
,,,,,,
,,,,,,
,,,,,,
,,,,,,
,,,,,,
,,,,,,
,,,,,,
Ǥޣ16碌ȣĻĤޤ
äơ̤ʾꤷĤǽϤޤ
101ڡ 20:20:11 43743
⡼ޥ
#43739 ܡʥꤵ
1*315ĤǤϤɤäƤ⡢ νĤĤʤȤȤ顢
3ĤȤȤ߹碌Ǥߤͤʤ褦ʡ?^^;
¨ ^^;v 101ڡ 22:57:24 43744
⡼ޥ
ޤ^^;;
ä¤٤Τ뤳ȤΤޤ
餷ޤOrz
¨ ^^;v 102ʶ 0:05:25 43745
ܡʥ
Ʊ褦 7x7 ˡ15 Ĥ1x3 Ĺ 1 Ĥ 3 ΤߤͤȡɤʤǤ礦

ߤˡϡʲΤ褦ʷǤ




102ʶ 2:45:22 43746
ǯ
#43743(Keigei)󡢤꤬Ȥޤ
Ф餷
dzä;ȤоɾˡȤȤƤפĤޤǤ
ɲü
ɤɤȿޤ󡣾嵭Τȡ󥰤κ˥áäȻפäΤϡ
΢֤ˤΤ΢֤ȡ֣ΣġפξˤʤΤϤʤǤ礦
֣ϣҡפξǤäƻĤ褦ʸ֤褦ˤפޤ
ΤˡºݤˤäƤߤȡޥʳΣޥĤˤϤɤäƤʤȤϳΤʤ褦Ǥ
ɤ⡢ºݤΣߣΥ֥å֤ȡ;꣱ΰ֤δطޤĤʤ

102ʶ 11:45:25 43747
???
Dim a(17) As Integer
Sub Macro1()
Cells(1, 1).Value = 0
Call saiki(1)
Cells(2, 1).Value = "=SUM(B1:B" & strr(Cells(1, 1).Value) & ")"
End Sub
Sub saiki(ByVal n As Integer)
a(n) = 1
While a(n) <= 3
For j = 1 To 7 : For jj = 1 To 7 : b(j, jj) = 0 : Next jj : Next j
x = 1 : y = 1
For j = 1 To n - 1
Select Case a(j)
Case 1 : b(x, y) = 1 : b(x + 1, y) = 1 : b(x + 2, y) = 1
x = x + 3
Case 2 : b(x, y) = 1 : b(x, y + 1) = 1 : b(x, y + 2) = 1
x = x + 1
Case Else : b(x, y) = 1
x = x + 1
End Select
QX = 0
While QX = 0
If x = 8 Then x = 1 : y = y + 1
If b(x, y) = 0 Then
QX = 1
Else
x = x + 1
End If
Wend
Next j
QX = 1
Select Case a(n)
Case 1
If x + 2 > 7 Then
QX = 0
Else
If b(x + 1, y) + b(x + 2, y) > 0 Then
QX = 0
End If
End If
Case 2
If y + 2 > 7 Then
QX = 0
Else
If b(x, y + 1) + b(x, y + 2) > 0 Then
QX = 0
End If
End If
Case Else
wa = 0
For j = 1 To n
If a(j) = 3 Then wa = wa + 1
Next j
If wa > 1 Then QX = 0
End Select
If QX Then
If n < 17 Then
Call saiki(n + 1)
Else
For j = 1 To 7 : For jj = 1 To 7 : b(j, jj) = 0 : Next jj : Next j
x = 1 : y = 1
k = 0 : j = 1
While k = 0 And j <= 17
Select Case a(j)
Case 1 : b(x, y) = 1 : b(x + 1, y) = 1 : b(x + 2, y) = 1
x = x + 3
Case 2 : b(x, y) = 1 : b(x, y + 1) = 1 : b(x, y + 2) = 1
x = x + 1
Case Else
k = x + 7 * (y - 1)
End Select
If k = 0 Then
QX = 0
While QX = 0
If x = 8 Then x = 1 : y = y + 1
If b(x, y) = 0 Then
QX = 1
Else
x = x + 1
End If
Wend
End If
j = j + 1
Wend
QX = 1
j = 1
While QX And j <= Cells(1, 1).Value
If k = Cells(j, 2).Value Then
QX = 0
Else
j = j + 1
End If
Wend
If QX Then
Cells(1, 1).Value = Cells(1, 1).Value + 1
Cells(Cells(1, 1).Value, 2).Value = k
End If
End If
End If
a(n) = a(n) + 1
Wend
End Sub
Private Function strr(ByVal n As Integer) As String
strr = Right(Str(n), Len(Str(n)) - 1)
End Function
102ʶ 11:32:56 43748
٥륯åĥ
ޥ뤵ǧڽͤǤ
9սʳξ֤ʤȤǧΤ֤Ǥ(Keigei)ˡϾꤤǤ͡ϻĤ7սˤĤơºݤ¤٤Ƥ̵ȳǧƤޤ
#43747Ԥ
鼺餷ޤ
Ȥ;012֤¤ǤΤǡ21֤Ȥ;012ξ꤬ɬ1սޤ롢äƺǸ˻ĤΤɬ;1ξǤꡢ;02ˤʤ꤬Ĥ뤳ȤϤꤨʤ
ǤǤ礦
102ʶ 12:41:37 43749
٥륯åĥ
#43735
ɤ餪֤
ǽ21ȴ㤤ƿޤ񤭻ϤƤޤǵŤƽľޤ
102ʶ 12:47:04 43750
uchinyan
#43739(#43746)
#43741Ʊͤ 400 ȻפޤΤʴ

7 * 7 Υޥܤ 1 * 3 Ĺ֤Υޥܤο¤Ͼ 3 ܿǤ
ξϤθˤäƷޤޤ 3 dzä;꤬ 012 Τ٤ƤǽǤŪˤϡ
3 dzä 0 ;롡ݡݡݡף

3 dzä 1 ;롡ݡݡݡף

3 dzä 2 ;롡ݡݡݡף

3 dzä 0 ;롡ݡݡݡף

ޤޤо꤫ΣĤθ¸ǽʤ¾ΣĤθ¸ǽǡ
Ĥθ٤ƤåȤǼ¸ǽǤ
ΤȤȡ1 49 ¤ 1225 3 dzä;꤬ 1 Ǥ뤳Ȥꡤ
Ĥ룱ޥο 3 dzä 1 ;Ȥ 3 dzä 0 ;ξǤäơ
оΤ֤¸ǽʤΤΤˤʤޤ㤨С
ף 1 <-----> ף 7Բġ
ף 1 <-----> ף 7Բġ
ף 4 <-----> ף 4Բġ
ף 4 <-----> ף 4Բġ

ף 10 <-----> ף 12ġף 10 <-----> ף 38ġף 10 <-----> ף 40ġ
ף 10 <-----> ף 12Բġ
ף 13 <-----> ף 9ġף 13 <-----> ף 41ġף 13 <-----> ף 37ġ
ף 13 <-----> ף 9Բġ

ף 16 <-----> ף 20Բġ
ף 16 <-----> ף 20ġף 16 <-----> ף 30ġף 16 <-----> ף 34ġ
ף 19 <-----> ף 17Բġ
ף 19 <-----> ף 17ġף 19 <-----> ף 33ġף 19 <-----> ף 31ġ

ɡ9, 10, 12, 13, 16, 17, 19, 20, 30, 31, 33, 34, 37, 38, 40, 41 16 ġǤ
塤7 * 7 ΥޥܤǤг˴ؤо⤢ޤ⥯ꥢޤ
ˡϡƥפ΢ФˤʤäƤĤмºݤ˼¸ǽǤ
ǡ
= 50 * 8 = 400
ˤʤޤ

ǸϾܤ㼨ޤ§оۤȤ餫Ǥ礦
ͥνȡ 102ʶ 16:04:00 43751
ǯ
#43749٥륯åĥ󡢤꤬Ȥޤ
Ƕ顩ˤɤͤ˻֤äƻޤ
äȤ󤬤Ƥߤޤޤʤˤ꤬դФ
102ʶ 13:46:34 43752
(Keigei)
#43747 Ԥ
#43743 ɤˤƤ⡢,ξФ˻Ĥʤ
ȹͤʬפΤޤ
103ڡ 0:38:40 43753
ܡʥ
ݤ߲³ǡֻ٤ޤޤäǡƱΤƤƤޤä褦ǡŤͽŤͿͭޤ

ᤤ (#43741)uchiyan (#43751) Ǥͤ᤬Ť褦Ǥޤ⡼ޥ󤵤 (#43744) Τ褦ʲͽۤϤƤޤ :-)

ñ㲽Τ 4x4 ޥǹͤޤߤͤ޷ 3 ĤǤǤƤΤǡ
ƥޥ 3 ǿʬޤʤ褦˿3 dzä;ο012 ɽޤ

ƥޥκɸ (0, 0) (3, 3) ɽ X ɸ Y ɸ¤ 3 dzä;οΥޥοޤơ 90 ٲžΤ 2 Ĥǹͤޤ

á
á
á
á

ȡ0 6 ġ1 2 Ϥ줾 5 Ĥġޤ1x3 ĹɤΤ褦֤Ƥ⡢֤줿 3 ޥˤɬ 012 ޤޤޤ

ʤΤǡ1x3 Ĺ 5 () ߤͤɬ 0 ΥޥĤޤοޤξȤ 0 ˤʤΤϡ4 0 ޥäơ 4 ĤΥޥΤ줫ĤȤǤޤ

ǯԤ (#43747) ʤξ 0 ˤʤޥȤȡ⤷ޤǻͶʳ 0 ΥޥĤ褦Ĺߤͤ줿Ȥơξ֤ 4x4 90 ٲžȡĤΥޥ κޤ 0 ǤʤޥξΤǡ̷⤹뤿Ǥ

˥ܡʥǤʲΤ褦˿ʬˡ򾯤Ѥޤ






1x3 Ĺ 4 Ĥ֤λĤäޥοοͤޤȡǸ˻Ĥ 1 ޥοϡλĤä 4 ޥοΤ줫ơĤȤ߹碌ϡʲ 4 ̤Τ줫

a) 4 ġ {400} ɽ (ʲƱ)
b) 3 ġ㤦 1 Ĥ {310}
c) 2 ġĤ 1 Ĥ {211}
d) 2 Ĥο 2 Ĥ {220}

Ȥǡϡɬ 2 ġȤϰ㤦 1 {210}֤ȻĤϡ 1 {100}

ΤȤ顢a) {400} Ϥꤨޤ (⤽⡢ 1 ľˤʤΤǤ֤ʤ)ޤ1x3 ĹĤ֤С֤줿ޥοƱ 3 ġ֤С֤줿ޥˤɬ 012 ޤޤޤʤΤǡ{400} ȤʤĤä 0 ǤꤨޤƱͤˡb) {310} Υѥ⤢ꤨޤ󤬡Ǹ 1 ޥȤľܴطޤ

ȤʤȡǸ 1 ޥϡ 2 Τɤоͤ (90 ٲž) ȡ̡ 2x2 ȤʤꡢǽŪ˻Ĥޥϡ 4 ޥΤ줫Ȥʤޤ

7x7 ξ硢ޤ 2x2 ˺Ǹ 1 ޥ¸ߤȤϸ¤ޤ㤨СʲA X Ǹ 1 ޥ

£££ãã
ģģģأ
ƣƣƣǣǣǣ
ȣȣȣɣɣɣ
ʣˣ̣ͣΣϣ
ʣˣ̣ͣΣϣ
ʣˣ̣ͣΣϣ

ʤΤǡ4x4 ǤԽʬǤ 7x7 Ʊͤ˹ͤȡ









15 Ĺ֤ĤΥѥϡϤꡢ a) d) 4 ̤ꡣơΥѥ {210} ˤʤΤǡ0 󤬽оͤȡĤλζʬˡǸ 1 ޥĤ뤳Ȥˤʤޤ

ա˻Ĥä 4 ޥˤοܤƤΤǡĹ֤塢Ĥä 4 ޥϢ³ƤɬפϤޤ

ơϡˡΤ褦ĹȤ֤뤫Ǥ7x7 ΤѤ顢4x4 ڤФĤ 33 ޥɬ 1x3 ĹǤ٤ʤĤޤʤΤǡ4x4 ǹͤ 2x2 ˤ֤ȤǤΤǡǸ 1 ޥɬĤλζʬ¸ߤ뤳Ȥˤʤޤ

ޤ7x7 ˤơ2 İʾΤѤ硢3 Ĥξ٤ƤΥޥǸ 1 ޥ뤳ȤǤޤ3 Ĥξ硢1472228434649 8 ʳΥޥǸ 1 ޥˤǤޤ
103ڡ 14:10:26 43754
ǯ
#43753(Keigei)󡣤äƤʤ顢ɤ⥹åǤޤ
Ф餯ͤƤߤޤ
103ڡ 21:36:23 43755
uchinyan
#43754
ܡʥꤵ
ܤ򤢤꤬ȤޤǤȻפޤ


䤢ᤤ (#43741)uchiyan (#43751) Ǥͤ᤬Ť褦Ǥ
#43751ϡɬ׾Ǹʤꡤ餬ºݤ˲ǽώʬǧƤΤǡ
Ūɬ׽ʬΤϤǡ־ͤ᤬Ť褦ǤפȤŦ褯ʬޤ
ɤʤΤǤ礦 ŦȹǤ
(֥ף 10פǤϥףΰ֤ϻꤷƤ餺 = 10 ڤƤޤ
Ǥ⡤ϰĤǽʬʤΤǡǤϤʤǤ͡)

䤪ޤ7x7 ˤơ2 İʾΤѤ硢3 Ĥξ٤ƤΥޥǸ 1 ޥ뤳ȤǤޤ3 Ĥξ硢1472228434649 8 ʳΥޥǸ 1 ޥˤǤޤ
Τˡɬ׾ǤϡİʾξϤ٤Ƥˤʤ褦Ǥ
¸ǽ褯ʬޤäˡĤξν룸Ĥ
ϤɤͤΤǤ
ͥνȡ 104 12:03:33 MAIL:uchi@sco.bekkoame.ne.jp 43756
uchinyan
#43755
ǯԤء鼺餷ƶ̤Ǥ

#43736ɽλ⤫ʤ㤤ޤ(Keigei)#43733ȹͤƱǤ
ɤ٤ĺ餴ΰˤʤ뤫Τޤ

ȡŪɽ񹳤ʤС󤵤#43738ʷǥåꤷƤȻפޤ
ĿŪˤϡ˲ˡȤ̣ǤϤͥƤȻפޤ

Ϸ̿ʤ顣
ͥνȡ 104 12:04:38 MAIL:uchi@sco.bekkoame.ne.jp 43757
ܡʥ
uchinyan (#43756)

䤬ͤ᤬Ťȴͳϡ䤬 #43754 ǼʲβʬǤƤʤȻפǤ

£££ãã
ģģģأ
ƣƣƣǣǣǣ
ȣȣȣɣɣɣ
ʣˣ̣ͣΣϣ
ʣˣ̣ͣΣϣ
ʣˣ̣ͣΣϣ

βˤơɤΤ褦ʡإףȣ <---> ..., ġ٤ȤɽˤʤΤˤǤޤǤñˡоפȸƤǼǤޤ

⤦ġ

> ޤޤо꤫ΣĤθ¸ǽʤ¾ΣĤθ¸ǽ
Ĥθ٤ƤåȤǼ¸ǽǤ

˼㤫餹ȡζˣ̻Τ֤ȤǤΤǡײ 90 ٲž ( γѤγѤ˰) ֤ȡ1 ޥĤ 15 Ĥ 1x3 Ĺ֤ȤϤǤޤ

Ĥޤꡢuchinyan #43751 ǽҤ٤줿ɬ׽ʬȤΤϡǽŪ˻Ĥ 1 ޥϾˤޤ 2x2 ˤȤȤΤ褦ˤ˴ޤ

ޤ (#43754) ְǤȻפޤפȤȤϡΤɤǼǤʤȤȤȤǤ͡ ǤСʬȤƤüޤäȤΤǡȽʤʬ򤴶ʤǤ礦

ޤ֤ޤפʬǤ 1 İʾϡץdzǧޤľʤȤ 1 Ĥξ⡢ޤ #43754 ǼΤäƤǡƤǤϼʬǤ䤽ξΤޤǤ̣ȤζǤ

2 İʾξǤ2 Ĥξϡ7x7 顢 2 ĤǤǤ 2x3 ĹڤäǹͤСϤܼۤȻפޤʳ⡢ƱͤˤǤ뤫ȻפޤʬǤ⡢3 Ĥλϡͽ۳ǤʤʤǡɤΡˡ
104 19:21:05 43758
ǯ
#43743, #43753(Keigei)#43749٥륯åĥ#43757uchinayn󡡤꤬Ȥޤ
ޥοѤơĴ٤Ƥߤޤ
3N+1ԡ3N+1ξüԡ3ˡ
3N+2ԡ3N+2ξˤϡǺǾ岼2ԡ2󤺤Ĥơ3M+1ԡ3M+1ηˤƤơüԡ3ΰ֤ˤʤ褦Ǥ
4445588Ϻ2󡢾岼2Ԥ44Ʊ֤ʤɤǤ礦
ΰ֤ϡ4ΤɤֹդƤ濴žоΤ;1Ǥ¾;1ξǤϻԺϰϤǤϡϤळȤǤޤǤ
֤Ϥ褯äΤǤоΤξȤƤ⡢¾оΤξϤäѤΤǤޤ߹礦礬äƤ⤤ȻפΤǤʤޤ߹礦ȤʤΤޤˤäȤƤޤ
伫ȡޤ;1,2,0ΰ̣Ȥ褯狼äƤʤȤȤʤΤǤ礦
̣Ǥ

105ʷ 8:37:45 43759
٥륯åĥ
¿ʬ򤵤ƤȻפΤǤϡֻĤޥȽ̤ˡפǤϤޤ
ֻĤȤǤʤޥȽ̤ˡפǤꡢʬ¤ϡ;02ȤʤޥĤȤǤʤפǤ
ŤͤƤߤȤ;꤬1ˤʤˤĤƤ̤ˡȤ334֤Ʒ֤31Ĺʤɤǡºݤ˻Ĥޥǧ뤳Ȥǡꤷޤ

⤷㤤ä餹ߤޤ
ޤְäƤФŦĺȹǤ
105ʷ 11:00:20 43760
tsk
#43758
ܡʥꤵء鼺餤ޤ

unityan(#43756)ϡ֥ףΰ֤ϻꤷƤ餺פȤΤȤʤΤǡβξ֥ף 13 פˤʤȻפޤ
ơֿޤоפʬ˴ؤƤϣߣΤǤäǤꡢƱײ90ٲžѤޤȡ

ʣʣʣȣƣ
ˣˣˣȣƣ
̣̣̣ȣƣģ
ͣͣͣɣǣģ
ΣΣΣɣǣģ
ϣϣϣɣǣأ
УУУţţţáʡ᥿ף 41

Ȥʤ뤳Ȥ򼨤ƤΤǤϤʤȼʬϲᤷޤǤΤʤȻפޤʴְäƤ餹ߤޤ󡣡

ޤ֤ޤפ˴ؤơ 214 ĤζξΤߤǤ 49 ޥ٤ƤˤƼ¸ǽ򸫤Ĥޤ

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ţƢʣʣ
ţƢˣˣ
ǣȣ̣̣̣ϣ
ǣȣͣͣͣϣ
ǣȣΣΣΣϣ

οޤDZΣߣʢӣʡСˤΤΣߣ򤽤줾ž뤳ȤǤ٤ƤΥޥˢư뤳ȤǤ
ܤΤ򣲡ߣ΢뤳Ȥ 4 սΤǤդξĤΤǤ٤ƤβսǸΣޥˤǤޤ
ޤãġţơǣȡʣˡ̣͡ϣФ򤽤줾줫Ĥؤ뤳ȤǤ 14 Ĥޤ䤻ޤ
ʤʤߤˡ7x7 顢 2 ĤǤǤ 2x3 ĹڤäǹͤפƤ⣱ߣĹ 2 ĤȤۤƱʤΤƱޥĤޤ󡣡
105ʷ 14:23:33 43761
uchinyan
#43758
ܡʥꤵ

ࡤǰʤ鴰˸ʤäƤ褦Ǥ
󡤤θϻۤˤΤǼȼʤ櫓Ǥ
ͤδܤ#43736ƱʤΤǤüޤäΤΤޤ
ޤƤޤ

7 * 7 ˽񤫤줿 1 49 ¤ 1225 3 dzä 1 ;Ǥ
Ĺ򤫤֤ȤΥޥܤο¤Ͼ 3 dzä 0 ;Ǥ
ǡĤ룴ޥο¤ 3 dzä 1 ;ˤʤޤ
ꡤο¤ 3 dzä;ꡤΥסˤäƻĤ룱ޥϹʤޤ
դߤΤϡȻĤδط;ǤӤĤƤ餺
ΰִطˤ;ʾβ󤬤ʤȤǤ
ˡоˤꡤ֤ȡ岼гоΤ֤ޤ
֤;ξ˽Τǡ˸䤬ʤޤޤǤɬ׾Ǥ
(žоΤϼоΤιDzǽʤΤǾάƤޤ)
ơ餬¸ǽȤʬ򼨤ޤ
ϼļФΤǡĤβǽ֤ΣĤ˸ڤ뤳Ȥˤʤޤ

ơǤ

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ʣˣ̣ͣΣϣ
ʣˣ̣ͣΣϣ

㼫ΤϡףX = 13ʤΤǡף 13; 0 + 1 = 1Ǥ
ơоˤꡤΥåȤǤޤܤ񤭤ޤ
ף 13 <--о--> ף 9; 1 + 0 = 1ġ
ף 13 <--岼о--> ף 41; 2 + 2 = 4 -> 1ġ
ף 13 <--ܾ岼о--> ף 37; 0 + 1 = 1ġ
гоΤޤƱͤưפ˥åǤΤǾܺ٤ϾάƤޤ
ף 13 <--夫鱦--> ף 37; 0 + 1 = 1ġ
ף 13 <--夫麸--> ף 13; 0 + 1 = 1ġ
ºݤˤϡгоΤǸΤϡ岼Ȥ߹碌鸽ΤפǤ

> ޤޤо꤫ΣĤθ¸ǽʤ¾ΣĤθ¸ǽ
䣴Ĥθ٤ƤåȤǼ¸ǽǤ
嵭ΰ̣ǤΣåȤǤ

˼㤫餹ȡζˣ̻Τ֤ȤǤΤǡ
䤽ײ 90 ٲž ( γѤγѤ˰) ֤ȡ
1 ޥĤ 15 Ĥ 1x3 Ĺ֤ȤϤǤޤ
ϤääƤ̣ޤҤȤäƤʤΤǤ
ΰ̣ʤСϥף; 2 ʤΤ 13 ȤޤΤ̵Ǥ

ξϡ3 dzä 2 ;ȤळȤˤʤޤ
ɬ׾˲᤮ʤΤǡ¸ǽϤޤ̤äǤ
äȹͤϰϤǤϡ17203841 ǤĹ֤餷̵
ʤ嵭Ρ
ף 13 <--岼о--> ף 41; 2 + 2 = 4 -> 1ġ
ϡΰ֤ŦȻפ롤֤Ȥϰ㤦ΤǼ¸ǽǤ
ĤޤꡤåȤΰ̣˸ʤäƤޤ

Ĥޤꡢuchinyan #43751 ǽҤ٤줿ɬ׽ʬȤΤϡ
ǽŪ˻Ĥ 1 ޥϾˤޤ 2x2 ˤȤȤΤ褦ˤ˴ޤ
Ȥ櫓ǡ餫˴ְ㤤ǤβˡϤäȰŪǤ

ޤ (#43754) ְǤȻפޤפȤȤϡ
ΤɤǼǤʤȤȤȤǤ͡
ǤСʬȤƤüޤäȤΤǡȽʤʬ򤴶ʤǤ礦
ʤ˲ᤷƤޤäΤǤäʤ顣

ޤ[400][310][211][220]εΰ̣Ǥ
㤨СĤ [400] ǤĤǤ⣲ĤǤ [400] Ǥ͡
ȣϣϸĿ㤦ΤǤΤʡȡǤ⡤ܼŪǤϤʤǤ
פäƤޤȡ
䤳ΤȤ顢a) {400} Ϥꤨޤ (⤽⡢ 1 ľˤʤΤǤ֤ʤ)
ޤ1x3 ĹĤ֤С֤줿ޥοƱ 3 ġ
䲣֤С֤줿ޥˤɬ 012 ޤޤޤʤΤǡ
{400} ȤʤĤä 0 Ǥꤨޤ
ޤǤOK
Ʊͤˡb) {310} Υѥ⤢ꤨޤ󤬡Ǹ 1 ޥȤľܴطޤ
[310] ΥѥϤ褦ʵޤ㤨СĤǣġ






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ģģģ

ǵΰ̣ʬʤʤޤޤܶڤǤϤʤΤ̵뤷 7 * 7 ˿ʤȡ

15 Ĺ֤ĤΥѥϡϤꡢ a) d) 4 ̤ꡣ
䤽ơΥѥ {210} ˤʤΤǡ0 󤬽
0 󤬽פͳ褯ʬޤۤɤ㡤

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ʣˣ̣ͣΣϣ

¿ʬΤ褦ˣؤϣˤʤȤȤǤ礦ԥȤޤ
ϡġġġ [211]Τ 90ž [310]⤢ޤ
ȤäƵΤǤ礦

оͤȡĤλζʬˡǸ 1 ޥĤ뤳Ȥˤʤޤ
ϷɤΤǤüޤ᤮Ȼפή줬Ƥޤ
ǽ;äΤǡ¿ʬΤȡ˲ᤷޤ
ϽפʤΤǡ޳ƳȤäƤ⤦ߺդߤǤ

ա˻Ĥä 4 ޥˤοܤƤΤǡĹ֤塢Ĥä 4 ޥϢ³ƤɬפϤޤ
Ǥ͡
ޤϡǸϥץʤΤǤ͡¸ǽĴ٤ˤϤ줷ʤΤʡ

2 Ĥξϡ7x7 顢 2 ĤǤǤ 2x3 ĹڤäǹͤС
ϤܼۤȻפޤ
ϤǤʤȻפޤ衣Ĥ 2 Ĥ룱ޥξͤƤߤƤ

ʤɬ׾Ǥ¤ϡܡʥξ⡤󤵤#43738μˡͭϤǸ̤⤤Ǥ
ˤʤĹʤäƤޤäΤǾάޤ̣ϹͤƤߤƤ
ͥνȡ 105ʷ 15:07:42 43762
uchinyan
#43761
tsk󡤹ͻ򤢤꤬Ȥޤ

#43756βϡоΤϼоΤ١ˤޤɤƱˤʤΤǡ̤Ǥ
򤤤Ƥ줷Ǥ ^o^

ʤۤɡ򸫤Ĥޤ͡㡪
ͥνȡ 105ʷ 15:33:45 43763
ܡʥ
tsk (#43761) uchinyan(#43756) ء

tsk 󡢡֥ף 13 ס̤ȻפޤʤΤǡ #43758 ΡǤޤǤפʬű

ơuchinyan ˤϼպפޤ

ֵͤ᤬Ťʬ˴ؤƤϰȤȤƤ⤷ޤ󤬡uchinyan ϲǽ򼨤ǡºݤˤ줬¸Ǥ뤫 (ĤޤꡢʳĹ򤹤٤֤Ǥ뤫) ƤʤȻפäƤޤʤ줬ֵͤ᤬ŤפȻפä֤ͳǤˡ

ơ #43754 ǤüޤäȤ⤢Τ (㤨С{400} ʤΤ 0 Ǥʤ{211} {220} ޤ 0 ǤˤʤˡդäɤΤ⤷ޤ

ޤtsk ˤϡǤ uchinyan #43763 ȯƤޤΥѥˤƱͤ˴㤷Ƥޤ

ȴְ㤤򼨤Ƥ볧ޤˤϴդǤ
105ʷ 16:57:54 43764
ܡʥ
tsk (#43761) uchinyan(#43756) ء

tsk 󡢡֥ף 13 ס̤ȻפޤʤΤǡ #43758 ΡǤޤǤפʬű

ơuchinyan ˤϼպפޤ

ֵͤ᤬Ťʬ˴ؤƤϰȤȤƤ⤷ޤ󤬡uchinyan ϲǽ򼨤ǡºݤˤ줬¸Ǥ뤫 (ĤޤꡢʳĹ򤹤٤֤Ǥ뤫) ƤʤȻפäƤޤʤ줬ֵͤ᤬ŤפȻפä֤ͳǤˡ

ơ #43754 ǤüޤäȤ⤢Τ (㤨С{400} ʤΤ 0 Ǥʤ{211} {220} ޤ 0 ǤˤʤˡդäɤΤ⤷ޤ

ޤtsk ˤϡǤ uchinyan #43763 ȯƤޤΥѥˤƱͤ˴㤷Ƥޤ

ȴְ㤤򼨤Ƥ볧ޤˤϴդǤ
105ʷ 18:34:48 43765
tsk
uchinyan(#43762,#43763)ܡʥꤵ(#43764)
㤬ä줿褦ǤʤˤǤȤβְäƤʤä褦ǰ¿ޤ

ޤޤ˴ؤơ˫ᤤ꤬Ȥޤ
Υѥ⸫ĤƤޤʲοޤǶѥ(#43761)ȤۤƱ򤷤ޤ
ޤϤĤξ硣



ãģ
ããģ

̻ʬϣߣȣߣηʤΤǾά 40 ޥޤޤơ

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ǣȣ̣Σϣϣ
ǣȣΣΣУУ

ޥޤꡢȤϻĤ꣸ޥԲǽʤΤǤġļʬ᤿ΤǤɤʤꤤޤm(_ _)m

ƣİʾδξǤ


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㣣
ããģ

15 ĤޤǤ٤ƾǤޤդƤߤФäǤ

ơǤ 16 İʳμ¸ǽ㤬·äȤˤʤޤϤƻĤƤȤˤޤ
ʥѥ̵õƤߤƤ
105ʷ 22:23:58 43766
ܡʥ
uchinyan (#43762)虜虜ǫ꤬Ȥޤtsk (#43761) λŦǡλפ߰㤤θäȤȽäΤǡʤ¤Ǥ

ơ #43754 ˤĤƤǤܻۤפä̤ȤŦƤ뤫Ȼפޤߤʬμĥ (ޤ) ȻפΤǡʤ٤ޤΤʤ褦Ȼפޤ

> 㤨СĤ [400] ǤĤǤ⣲ĤǤ [400] Ǥ͡

ϤɽϤǤĤ 4 ޥͤˤϡ4 ĤȤʤΤϡ˸¤ޤλ¤顢{400}
0 4 Ĥȡ򤵤ƤޤΤϡɽΤޤ˴Ƥޤ

> [310] ΥѥϤ褦ʵޤ㤨СĤǣġ

⡢ ̤ǡ{310}{211}{220} ޤơפȽ񤯤٤Ǥơuchinyan ŦƤ褦ˡ礭üޤäȤǤ

> 0 󤬽פͳ褯ʬޤۤɤ㡤

⤦ޤΤʤˡǡ򤷤Ƥߤޤ

ǽŪ˻Ĥ 1 ޥ4x4 ǹͤޤγƥޥˡΤ줫ʲΥѥǽ줿̤ǹͤޤ






θĿ 8 ġθĿϡ줾 4 ĤĤ뤳Ȥˤʤޤ

̤ 1x3 Ĺ 4 ֤ĤΤ 4 ޥǤơλĤä 4 ޥˤ֤Τʤ顢 4 ޥΤ줫Ǹ˻Ĥ 1 ޥˤʤޤ

ǡ1x3 Ĺ 1 Ĥʤ 3 ޥεθĿͤȡĤ֤硢Ʊ椬 3 ġ֤硢ۤʤ뵭椬 3 (Ĥޤꡢ 1 Ĥ)

ΤȤ顢Ĺ򤤤Ĥ֤ʤƤ뵭θĿ򡢤줾 abc ȤȡʲδطΩޤ

a b c (mod 3)

ޤĹ֤Ƥʤޥˤ뵭θĿ򡢤줾 pqr ȤȡιƱΤ˽񤫤Ƥ뵭θĿ顢ʲδطΩĤȤȽޤ

p+2 q r (mod 3)

ǡʹߤΤᡢ뵭椬 x ġʳ 2 Ĥε椬줾 y Ĥ z Ĥ뤳Ȥ򼨤ɽ {xyz} ƳޤɽˤƤϡxyz 줾ɤεθĿǤ뤫ꤷƤޤ

ɽѤ1x3 ĹʤθĿϡ{300} () {111} () ɽޤ

ƱͤˡϤɤΤ褦ʸ֤Ƥ⡢{210} ȤʤꡢǸ 1 ޥ {100} ȤʤޤơΤǤ {844} ǡ8 ĤʤΤϡǤ

̤ 1x3 Ĺ 4 ֤Ĥä 4 ޥϡ{400}{310}{211}{220} Τ줫ˤʤޤơ 2 ܤιƱȤ {210} Ǥ뤳ȤθȡʲΤȤƳޤ

{400} λƱ 4 ĤʤΤϡǤ롣 {210} Ǥ뤳Ȥ顢֤ȤǤʤ

{310} λƱ 1 ĤʤΤϡǤ롣ơ {210} Ǥ뤳Ȥ顢֤ʤɬʤäơǸ 1 ޥεϡǤϤʤ

{211} λƱ 2 ĤΤϡǤ롣ơ {210} Ǥ뤳Ȥ顢֤ʤɬ 2 ĤΡʤäơǸ 1 ޥεϡǤϤʤ

{220} λƱ 0 ĤʤΤϡǤ롣äơ֤ʤСǸ 1 ޥεϡǤϤʤ

ʾ夫顢Ĥä 4 ޥˤ֤뤹٤ƤξˤĤơȽ񤫤줿ޥǸ˻Ĥ 1 ޥˤϤʤʤȤȽޤƵν񤫤줿̤ 90 ٲžΤǹͤȡǸ˻Ĥ 1 ޥ 2x2 Τ줫Υޥˤʤ뤳ȤȽޤ

ޤǺǸ˻Ĥ 1 ޥ¸ߤ뵭ˤĤƲǽҤ٤ƤΤǡºݤĹȤ֤ʤߤͤ뤳Ȥ¸ǽǤ뤳Ȥ򼨤ɬפޤ

ºݻƤߤȡĹ 4 Ĥλ֤ȡ 2x2 ĤȤǤ롣ޤ 2x2 ˡ٤ƤθΤ֤ȤǤ2x2 4 ޥ٤Ƥ򡢺Ǹ 1 ޥˤ뤳ȤǤޤ

äơǸ 1 ޥϡ 2x2 ˴ޤޤ 4 ޥˤʤ뤳Ȥˤʤޤ

7x7 ξ⡢ƱޤƾεΩޤΤǡǸ 1 ޥ¸ߤǽޥϡĤλζʬˤ 4 Ĥ 2x2 ˴ޤޤ뤳ȤȽޤ

줬˼¸ǽ򡢤Τޤ޻ΤϹޤΤǡפ򤷤ޤ

7x7 λͶ 1 Ĥ顢4x4 ڤФޤȡĤä޷ˤ 11 ĤĹ֤ʤߤͤ뤳ȤưפȽޤ4x4 ˤƤϡ4 ĤĹ 1 ĤΤߤͤ뤳ȤǤ2x2 ˴ޤޤ뤹٤ƤΥޥǸ 1 ޥˤ뤳ȤǽǤͶΤ٤ƤǻСĤλζʬˤ 4 Ĥ 2x2 ˴ޤޤ뤤줫ΥޥǸ1 ޥˤ뤳ȤǤޤ

2 İʾΤǤϡμˡǤϾʬȯŪơŪǤϤʤȻפޤ

ŪʬʤΤǤAnalytic Combinatorics (ܸɤ狼ޤ) ȤΤޤȯŪʬ¿༰ʣǿ¿ѤƥޡȤ˽ˡΤ褦ǤˤĤƤϡӡ񤭤ޤ
106ʲС 6:12:55 43767
uchinyan
#43764#43767
ܡʥꤵ

򤤤褦Ǥ褫äǤ
ޤͤ᤬Ťΰ̣򤷤ޤ

ϻʸ⤢ΤǤƱǡĤ룱ޥ򤷡
Ū֤ޤǤϾܺ٤Ĵ٤ȤǧƤޤǤ
äơɵᤷɬ׽ʬϻĤ룱ޥƱꤹΤɬ׽ʬʤǤޤ
ˤǧΥ줬äȻפޤ
Ū֤򤹤٤ƵȤʤȡʤʤѤˤʤꤽǤ

ˤ衤򤢤꤬Ȥޤ
Ԥ㤤ϤäȤϤȵǤƤ褫äǤ
ϥޥ뤵󤬽ꤵ꼫ζ̣Τ¿ΤǤ
ޤ򤯤ȡƲ򤱤ǼĤdzβˡ򸫤뤳ȡ䲿餫ȯŸ뤳ȡʤɡ
ڤȡٶˤʤ뤳ȡ󤢤ޤ
ޤϤ󶡤Ƥޥ뤵˴աƻä볧˴աǤ

ޤ#43767Ǿܤɲäβ򤢤꤬Ȥޤ
ǰʤ֤줺ˤޤɤƤʤΤǤǤäɤޤƤ

#43766
tsk

ޤ򤽤ʶ򸫤Ĥޤ͡
ޤɤƤʤΤǤǤäɤޤƤޤ

󡤤줫⵹ꤤפޤ
ͥνȡ 106ʲС 15:07:41 MAIL:uchi@sco.bekkoame.ne.jp 43768
ܡʥ
ޤtsk (#43766) ء

ǽѥŪʤθĤ줿ƶϤ˷ޤ

uchinyan (#43768) ء

> Ū֤ޤǤϾܺ٤Ĵ٤ȤǧƤޤǤ

伫Ȥ⡢Ū֤ܺ٤Ĵ٤ȤǧƤޤ󡣤ʤʤ顢uchinyan Ĥ褦ˡƤβΤϷ빽ѤʤΤǡ

ɤȸ뤫⤷ޤ󤬡⤦դ礤

䤬äͳ⤦ޤϡĹȤϰۤʤꡢǽ餫֤ʤȤ¸ߤޤ䤬ǽ˻Ȥäʲοޤ򸫤Ƥ






οޤǤϡ0 6 ġ1 2 5 ĤġĹɬ 012 3 ĤοʤޤΤᡢǽˤ 0 Ǥʤ 2 ĤƱʤ褦֤ƤޤȡĹ 4 Ĥ֤뤳ȤԲǽˤʤޤ

о (ޤ 90 ٲž) ͤȡϻפä긷Τˤʤ뤳Ȥ狼뤫Ȼפޤ

­Ǥ䤬ĹξˤοޤѤΤϡ֤Ǥʤ꤬뤳ȤؤΥҥȤǤ⤢ޤ

uchinyan Ѥ줿;οδطǤ֤ʤӽǤƤʤȻפޤʤΤǡ֥ףȣ IJġפȤΤϡ֥ףΤ 1 ĤĹ 15 Ĥ֤ˤϡǸ˻Ĥ 1 ޥˤ뤳ȤϲǽפȸäƤ˲᤮ʤ򤷤Ǥ

ΤᡢºݤˤΤ褦֤ǽǤ뤫򸡾ڤɬפȻפäǤ

βˡǤƱǡ֤Ȥ顢ޥǸ 1 ޥˤʤʤȤڤƤʤΤǡڤɬפǤ

ڼΤϡ4x4 ξ礫顢ܼۤ˶ᤤΤǡñ˳䰦Ȥϻפޤƺ١ֵͤ᤬Ťפȸ碌ĺޤ

­Ǥ⤽λθ uchinyan 󤬤ΤǤϤʤ䤬˼򤬡֥ף 12פˤʤȴ㤤Ǥ (1 ǤϤʤ0 Ƥޤä)Τ˺𤷤ƤޤǤ򤪤ƤޤäȤŤͤƤͤפޤ

餳uchinyan tsk Ϥᡢդ礤ĺ󤢤꤬Ȥޤͤdzڤ֤ᤴȤǤޤ

ϻϰϤ礭æޤ줿 Analytic Combinatorics μˡѤơ4x4 ˤ 1x3 Ĺ 5 Ĥߤͤ᤿λĤ 1 ޥͤޤ

ޤƥޥ (0, 0) (3, 3) κɸ򿶤ޤǤϡ (0, 0) (0, 3)夬 (3, 3) ˤʤ褦ˤޤ

˰ʲ¿༰ͤޤ

1) f(u, v) = (1 + u + u^2 + u^3) * (1 + v + v^2 + v^3)

¿༰Ÿ u^x*v^y ο 16 Ȥʤꡢ (x, y) ޥκɸɽޤ (1 ϡu^0*v^0 Ȥɽ)

ʹߡu^x*v^y {x,y} ɽȤˤޤ

ĹĤ֤

{x,y} + {x,y+1} + {x,y+2} = {x,y} * ({0,0} + {0,1} + {0,2})
= {x,y} * (1 + v + v^2)

֤硢Ʊͤˡ

{x,y} + {x+1,y) + {x+2,y} = {x,y} * (1 + u + u^2)

ȡǽ¿༰ϡ

2) f(u,v) = (1 + u + u^2) * g(u,v) + (1 + v + v^2) * h(u,v) + {x,y}

ɽޤ ǡg h ϡu v ¿༰ͤȤؿǤơǸ {x,y} Ǹ˻Ĥ 1 ޥκɸɽޤ

w 򡢼βȤޤ (w ϡ1 λ躬)

1 + w + w^2 = 0

w 򤽤줾졢 1 ȼ 2 Ϳޤ

f(w,w) = (w^3) * (w^3) = 1

f(w,w) = w^(x+y)

ʤΤǡ

x + y 0 (mod 3)

Ʊͤˡw^2 w 2 ĤμͿޤ

f(w^2,w) = 1

f(w^2,w) = w^(2*x+y)

ʤΤ

2*x + y = 0 (mod 3)

2 ĤιƱ顢

x 0 (mod 3)

ơx 0 3ơy 0 3 Ƚޤ

ʤΤǡǸ˻Ĥޥκɸϡ(0,0)(0,3)(3,0)(3,3) 4 ġ

7x7 ƱͤˤơϤƱƱΤǡx ϡ036 Τ줫ơy 036 Τ줫Ƚޤ

ޤNxN ξ硢

N 1 (mod 3) ǤС 1 Ѥǡ 2 ĤιƱ 4x4 ƱΤʤΤǡĤޥκɸϡ x y 0 (mod 3)

N 2 (mod 3) ǤС 2 ĤιƱ

x + y 1 (mod 3)
2*x + y 0 (mod 3)

ȤʤΤǡĤޥκɸϡ x y 2 (mod 2)

ϡǯԤ #43759 ͽۤȤפޤ

Τ褦ˡAnalytic Combinarorics ΤȤϡμ 1 2 ٤С1 沾躬Ȥäơ٤Ƥξ뤳Ȥ֤ǤǤƤޤȤǤ

ȥåʤȤ¿ޤ򥭥ˤʣDzϤΰƧ߹ޤʤȤʤΤǡǤϳ䰦ĺޤ (Ȥϡ伫Ȥμˡ򤷤ƤʤΤǡ뼫ʤΤǤ)ñˡΤ褦ʲˡ⤢Τ򤷤Ʋ
107ʿ 7:17:20 43769
ܡʥ
ǯԤ (#43759)ⲣ鼺餷ޤ

> ֤Ϥ褯äΤǤоΤξȤƤ⡢
> ¾оΤξϤäѤΤǤޤ߹礦礬ä
> ⤤ȻפΤǤʤޤ߹礦ȤʤΤ
> ˤäȤƤޤ

ʤȤȡ3N+1ԡ3N+1ξϡ٤ 4x4 ˡ
3N+2ԡ3N+2ξϡ٤ 5x5 ˵夹뤫Ǥ

㤨С7x7 ϡͶΰĤ 4x4 ڤФȡ
ڤ줿ο޷ϡĹǤ٤ʤȤǤޤ
ξ֤Ǥ 4x4 ˤƻĤޥ7x7 ǻĤޥ
ʤꤨޤ

򡢻Ͷ٤ƤˤĤƹͤȡ7x7 ƤΥޥ
åȤˤʤꡢ֤žоΤˤʤ뤳ȤȽޤ
Ʊͤ 10x10 ξ⡢7x7 ڤФСƱͤΤȤޤ

8x8 ξ⡢5x5 ڤФƹͤƱͤˤʤޤ

ޤĤˤĤƤͽۤǤ

NxN γƥޥX-Y ɸ
(0,0)夬 (N-1,N-1) Ȥʤ褦ˤȤȡ

N 1 (mod 3) λ
Ĥޥκɸ (x,y) ϡ x y 0 (mod 3)
N 2 (mod 3) λϡx y 2 (mod 3) Ȥʤޤ

줫⡢˰βžоΤΥѥˤʤ뤳ȤȽޤ

⤷̣Сξ #43769 θȾˤޤ
Τǡ (ˤäƤϡغ𤹤뤫⤷ޤ
ξǤϼ꤫ͤޤΤͽᤴλ)

ȡ;̤Ǥ䤬βդ򤷤Ƥˡ
AND Ȥ̣Ǥʤ̤¿ޤ

λˤϡˡȤäΤ褦򤷤Ƥޤ

ѥ󤬥ޥ˽񤭹ޤ줿ξ
Ĺ֤Ƥ ĹǸ 1 ޥ
Ĥ֤Ȥޤ

θ塢ˤѥ󤬽񤭹ޤ줿
90 ٲžޤ

λκǸ 1 ޥѥ󤬽񤫤줿
֤ʤޥ˰ưʤ顢̷⤷ޤ

ʤΤǡž (뤤ϡȿž) ΤȤζˤʤޤ

ºݤˤϡƩʲߤӥˡ˻ĤʾΥޥ
դơ±餵Τ̤ƤǤ

ޤƱˤʤ 180 ٤ 270 ٲžΤĴ
ʤƤɤˤʤꡢĻǤ
107ʿ 9:24:38 43770
ǯ
#43760٥륯åĥ#43770ܡʥꤵ󡢤꤬Ȥޤ
44558810101111ȤäƤơ4455˵夹뤳Ȥ鲿ΤǤϤȤȤޤޤ褬狼ޤǤޤǤƤʤȤ⤢ޤΤǡ褯ɤޤƤޤ
107ʿ 11:41:59 43771
uchinyan
ܡʥꤵ

ʹͻ򤢤꤬Ȥޤ
ä˸Ⱦε򤽤ʤΤǸǤäɤٶƤ

ʤβˡ˴ؤƤϡ

uchinyan Ѥ줿;οδطǤ֤ʤӽǤƤʤȻפޤ
ʤΤǡ֥ףȣ IJġפȤΤϡ
֥ףΤ 1 ĤĹ 15 Ĥ֤ˤϡǸ˻Ĥ 1 ޥˤ뤳Ȥϲǽ
ȸäƤ˲᤮ʤ򤷤Ǥ
ϤϤä̤ǡɬ׾˲᤮ޤ

䤳ΤᡢºݤˤΤ褦֤ǽǤ뤫򸡾ڤɬפȻפäǤ
Ϥ⤪ä̤ǡνʬΥåɬפǤ
ؤιͤ˰㤤äޤ줿ǧƤޤ
ϼΤ褦˽μˡΤΤޤ

¸ǽ֤ν Aоޤ᤿;ξ֤ν Bף 13 ֤ν CȤޤ
A B ˴ޤޤ졤C B ˴ޤޤޤޤǤɬ׾Ǥ
Ǥ A C δطʬޤ󡣤餬νʬǤ
ϻĤ룱ޥƱꤹ뤳ȤܻؤΤǡA C ζʬɤȽꤷޤ
Ǥʤ 13 Ĥ뤫Ǥƶɤǡ㤬ĤǤ⤢뤫򼨤нʬǤ
θʬϤΰ̣ǡʬ䤹 2 * 2 ˤ 13 ˸ڤޤ
ήǡͤ᤬ŤȤȽˤ񹳤ޤ

2 * 2 ˤ 13 ʤ˸ڤ褫äΤΤޤ
ޤä褦ˡC ˤ A ˴ޤޤʤΤ⤢Τǡͻڤ餷ʤäΤϡ
ͤ᤬ŤȤȽƤפʤʡȿʤ⤷Ƥޤ



ǡäȻ֤줿ΤǡȾ Analytic Combinarorics ȤΤ򸫤Ƥߤޤ

N 2 (mod 3) ǤС 2 ĤιƱ
䡡x + y 1 (mod 3)
䡡2*x + y 0 (mod 3)
ȤʤΤǡĤޥκɸϡ x y 2 (mod 2)
Ǹ mod 3 Ǥ͡

Τˡ򤤤Ǥ

Ʊ̤ϡ󤵤#43738ǤäƻΩƤʤƳ褦Ǥ
(ɸ 1 ƤΤա)

¿ʬAnalytic Combinarorics ٤ȯŸΤǤ礦͡
ͥνȡ 108ڡ 11:14:14 43772
ʪ
٤ʤޤ
100n+25֤ĤǤ
108ڡ 0:02:14 MAIL:butsuri.0523@gmail.com HomePage:Math Labyrinth 8󹹿43773
ʪ
Ȥפޤ֤Ĥᤤ
ȻפԼ...
108ڡ 0:04:40 MAIL:butsuri.0523@gmail.com HomePage:Math Labyrinth 9󹹿43774

ϵ٤ߤȡȤʤνǤ򸫤ƤߤȯŸƤơɤǤߤΤǤǰʤۤȤǤˡФΤϸ꤬Τȥޥ뤵ˤ餿ƴաǤ
ܡʥꤵؤβǻ̾ФƤΤǡʣߣޥĴ٤ȤñʡŪǤϤʤˡˡߤʤε˴ޤޤƤΤ狼äƤʤΤǤߣޥ򲼿ޤΤ褦ˤ
££
££
££
££
££££££
££££££
££££££
ΣޥɤˤäƤžУΣߣޥꡢ¤ʬϣߣޥǥСǤΤǡΣߣޥĴ٤ФȹͤޤʤΤꡢɬ׽ʬȤޤǤˡ

Ϻꡡ 108ڡ 6:01:43 43775
Mr.ǥ
ϽʤȤȤǡȤȤǸҲ𤷤ޤ
ʾʬݤˤʤäΤǡꥹޡȤʲˡϤʤΤȻפäƤޤ

ۣĤΥA,B,C򿶤äȤܤѤ12ܿˤʤοƲ
108ڡ 11:35:56 43776
uchinyan
#43775

¿ʬŪʹͤϡܡʥꤵƱȻפޤ

#43776
Mr.ǥ
91 ̤꤫ʡ
ĥľʬƿ񤷤ϤʤǤΤ˥åȲ򤱤ˤʤʤ
ͥνȡ 108ڡ 12:39:53 MAIL:uchi@sco.bekkoame.ne.jp 43777

#43776
Mr.ǥ
ɥåꤤʤäΤǤuchinyanƱˤʤäΤDzˡ򵭤ޤ

12ܿˤʤˤ(1)1ĤΥܤ6
(2)1ĤΥܤ3ˤʤȹͤޤ
(1)Ĥ2ĤξʤȤ1ĤܤǤФ褤
66-33=27
6ܤA,B,C̤ʤꤦΤ273=81
(6,6,6)νʣʬ2
(6,6,a)(a=1to5)νʣʬ35=15
81-2-15=64̤
(2)(3,4,a)(a=1to6)ξ礫(3,3,4)(4,4,3)νʣʬ
66-23=30
4ʤĤܤɬ26ˤʤΤ
(3,2,6)=6(3,a,a)=32=6(a=2,6)
ä30+6+6=42̤
(3)63ʣʬ
(3,4,6)=6(3,2,6)=6(3,6,6)=3
(1)+(2)-(3)=64+42-6-6-3=91̤
ȤϤʤޤĥޡȤʤΤʬޤǤ

108ڡ 13:54:08 43778

#43776
Mr.ǥ
⣹ˤʤޤ
գΩΤIJ⤵ĤѤ߽ŤʤäΩΤ򥤥᡼ܤܿΥޥϤ줾죶ĤΣܿäƤȹͤΤǤξʬǤ
108ڡ 17:40:23 43779
⡼ޥ
#43776
Mr.ǥ
ߤʤ91...
6^3-5^3=91
ʤΤ...
̣դͤƤߤޤ狼ޤ^^;;
ޤޤʤǤ礦?...
¨ ^^;v 108ڡ 19:17:51 43780
ǯ
#43776 Mr.ǥ
㲽褦Ǥߤޤ󡣿ʾʬƤߤޤʬͤƤǻ֤äƤޤɡ郎ǤᤫäIJΣޥоΤʤΤɬפʤΤϣޥˤ׵礦ο񤭹ǿ

#43770ܡʥꤵ
Ĥ褦ǿޤ󤬡ϤꤦޤǤޤ
ʤȤȡ3N+1ԡ3N+1ξϡ٤ 4x4 ˡ
3N+2ԡ3N+2ξϡ٤ 5x5 ˵夹뤫Ǥ
㤨С7x7 ϡͶΰĤ 4x4 ڤФȡ
ڤ줿ο޷ϡĹǤ٤ʤȤǤޤ
䤽ξ֤Ǥ 4x4 ˤƻĤޥ7x7 ǻĤޥˤʤꤨޤ
ˡϽʬǤϤ뤫Τޤ󤬡ɬ׽ʬȤ뤫ɤ
ĤθϣߣǤ飵ߣڤФƹͤ뤳ȤǤޤξ¦飲ޥĤȤäΣߣȹͤ뤳Ȥޤ̤ƱˤʤΤǡ餫δطȤϻפޤΰ̴طξΤ狼ȤäʤʬǤ
Give-Up!

108ڡ 20:30:17 43781
⡼ޥ
#43776 Mr.ǥ
祦Ǥ ^^;;
ʲ...

㣲Ȣɬ...
12=2^2*3=2*2*3 or 2*6 or 4*3
2233̤
26x2623̤ꡢ266̤ꡢ26(1,3,4,5)4*6̤=30̤
433,4342*3=6̤ꡢ43(1,2,5,6)4*6=24̤=30̤

24=4*6
464,466, 46(1,5)=3+3+2*6=18̤

36=6*6
666,66(1,3,5)=1+3*3=10̤
=3+30+30+18+10=91

ǤΤ? Orz
׻ְ㤤(ɡ)䤳...
¨ ^^;v 108ڡ 21:15:30 43782
Mr.ǥ
uchinyanJޥޤ󡢤ᤤ󡢺ǯԤ󡢥⡼ޥ󤵤󡡼ȤǤͭ񤦤ޤ
줫顢ߤʤβˡäɤޤƤȻפޤȤꤢβˡ񤭹Ǥޤ
--------------------------------------
63ĤΤȤ(6,6,6)1̤
62ĤΤȤ{6,6,}ʡ:15ˤ¤ؤ.....5*315̤
61ĤΤȤ6Υ3̤
¾2Ĥ 15ǡʤȤ1Ĥϡ2or4 ....5^23216̤
ס3*1648̤
60Ĥξ
{3,3,4}{3,4,4}{3,2,2}¤٤Ρ......3*39̤
{3,4,}(1,2,5ˤ¤ؤΡ.......3*3!18̤
ס27̤

ꡡ1+15+48+2791̤
ʤβˡդǤ
108ڡ 20:38:36 43783
ܡʥ
٤ʤޤuchinyan (#43772)
ᤤ (#43775) ǯԤ (#43781) ؤǤ

ˡ֤ޤ

ޥ뤵θ (裹) ¿γ󤬡;
ƳФƤ뤫Ȼפޤɤʤ
ºݤ˼¸ǽ˿Ƥʤ褦˸ޤ

uchinyan ϡФƤϡ˲ǽ򼨤줬
¸ǽǤ뤳Ȥ򼨤ȤƤޤ

ʤΤˡʤ󡢸Ǥϡ򤷤ƤʤΤǤ礦 ?
ɤʤʬ䤹ĺޤ ?

ʤϡ¸ǽǤ뤳Ȥ򼨤ˤϡºݤ֤򼨤
ʳˡʬޤǤ äȥޡȤˡ
Ǥ礦 ?

ޤǤ֤Ǥ

ǽˡuchinyan #43772 Ф롢Ǥ

> ؤιͤ˰㤤äޤ줿ǧƤޤ

󥫤褦ǿʤΤǤϡؤιͤ
Ф̵ǧƤޤ

ͤ㤨 uchinyan βˡϡǽ˲ǽ򼨤
줬ǽǤ뤳Ȥ򼨤ȻߤƤޤ

ͣΰ㤤ϡuchinyan ϥȥ졼Ȥ˻ĤޥõΤФ
ϻĤʤޥõȤǤ

ǡβˡ uchinyan βˡͥƤ뤤ȡ
ϴƤޤ

Ȥ顢̤ΤȤˤȻפޤ
ĺȻפޤ

> ϼΤ褦˽μˡΤΤޤ

ˤĤƤεΤˤϡä˰Ϥޤ󤷡θڤǤ
ƱͤʼˡȤäƤޤ (һ)

ǽ顢ΤȤǤʤ򤬤äΤǡ虜虜֤Ȥ餻
ƤޤäΤǤϤʤȡ̤Ƥޤ

䤬ääΰʲʬ

> θʬϤΰ̣ǡʬ䤹 2 * 2 ˤ
> 13 ˸ڤޤ

ʬտޤϽʬǤޤ #43751 ǤƱͤǤ

> ήǡͤ᤬ŤȤȽˤ񹳤ޤ

դ֤褦ʤΤǤꡢΥѥ󤬡֥ף 13
νä°뤳Ȥ餫Ǥ줬¸ǽʽ˴ޤ
뤫ɤϡޤǤʤä褦˻פޤ

⤦ȡunchinya 󤬡ɤΤ褦ˤ 7x7
ˤ 1x3 Ĺ 15 ֤ơ˹פ 2x2
ĤȤǤȽǤΤˤǤʤΤǤ

äȤ⡢7x7 λͶΰĤ 4x4 ȻĤʬͤСۤ
Ǥᤤ󤬤Ǥ #43741 4x4 Ǽ¸ǽǤ뤳
˸ڤƤȤ⤢ΤǡǤϼʤȤȤ䰦
줿򤷤Ƥޤ

ϡ伫ȤͤˡǤƱǡˤΤ褦ʥޥĤ
֤ΤϤޤǤ顢ץȤǸ
ڤƤߤΤǤ

ơǽơ4x4 ˵夹ȵդ򤫼ԤǤ⤢ޤ

䤬פֵͤ᤬ŤʬǤ
ñˡֵͤ᤬ŤפȤΤǤϤʤεľŪ˽񤯤٤
ȡϻפäƤޤ

䤬ͤˡȤСǤϤʤǤ礦 ?

⤷䤬ޤ㤤Ƥ褦ǤС
ĺȤ꤬Ǥ

ޤǤ⿨ޤ #43767 θʬƱǤ

ʤʤ顢Ĺ֤ȤλĤ 4 ޥˤĤơ
εˡ {310} Ǥϡ֤Τϡˢ 3 Ĥλ
⤷ޤ (̻ĤΤϢ)
Ʊͤ {211} {220} Ǥ⡢ĤΤ ʤΤ⤷ޤ

Ȥ4x4 ǹͤȡŪ˾ {220} 2x2
ĤȤǤޤ{220} 2x2 ˼ޤäƤΤʤ顢
Τ٤ƤΥޥǸ˻ĤȤǽʤȤϤܼۤǤ

ǡƾǤȻϹͤƤޤ

ʤθڤǤϡ{310} {211} ξθڤޤ
ϡuchinyan Ʊͳ (Ȼ䤬˻פäƤ) ǡ
פȽǤǤ

ƤΤϡĤޥǤäơɤˤ֤뤫Ǥ
ʤΤǡ

ΡԤޤΤʤ ޤޤԽʬǤ
ޤޤʤ­ޤ͡ȿʡ

> Ǹ mod 3 Ǥ͡

ֵͤ᤬ŤפǤ͡ɤƼϤ

> Τˡ򤤤Ǥ

Analytic Combinatorics Ǥ ?
δư˶Ƥơ˴򤷤Ǥ

ޤ󤵤 #43738 ˤĤƤϡ3 dzä;
񤭹ѥȤäǧƤ
ޤ

> (ɸ 1 ƤΤա)

ڤᤢ꤬ȤޤǡѤʸ򤷤
ǺѤߤޤ

ˡᤤ (#43775)ͤϡ򤷤ƤĤ
ǤơŪˤȤuchinyan ⼨
ޤ

ᤤˡǤϡ4x4 ˡĹ 1 ޥ
Ĥ 4x4 Ϥ߽Ф뤳Ȥʤ֤˸¤


#43758 ǼʲΤȺǸ˻Ĥ 1 ޥ
4x4 ˼ޤʤ礬ޤ

£££ãã
ģģģأ
ƣƣƣǣǣǣ
ȣȣȣɣɣɣ
ʣˣ̣ͣΣϣ
ʣˣ̣ͣΣϣ
ʣˣ̣ͣΣϣ

ˡȺǸ 1 ޥ4x4 ˼ޤ褦 DDDX
ȿžƤ⡢ĹΤĤϤ߽ФƤޤޤ

ʤΤǡ4x4 ­Ӥ 7x7 ǤƱȤϡڤʤ
ϻפäƤޤ

ǸˡǯԤ (#43781) ء

> ˡϽʬǤϤ뤫Τޤ󤬡ɬ׽ʬȤ뤫ɤ

üޤ᤮褦ǤʲΤ褦˹ͤޤ

뷿 (3N+1 3N+2) ˤơ1x3 Ĺ򤤤Ĥ
Ŭ֤ơ꾮 3N+1 3N+2
ĤȤǤȤޤξ硢⤷ξԤǻĤ
ΰ֤ۤʤäƤС̷⤷ޤʤΤǡξԤλĤޥ
ΰ֤ɬפޤ

ޤ3N+1 3N+2 ξȤ⡢ʬƱǡʬ
1 (N-1) 򤹤٤ƤλͶ˻ĤȤǤޤ
(1 ٤ 1 Ĥ)

ʤʤ顢礭顢ΰϡ
3x(N-1)(N-1)x3 Ĺ 2 Ĥ 3x3 1 ĤʬǤ
Ϥ٤ơ1x3 ĹǷ֤ʤʤȤǤΤǡ

龮 4 Ĥǡ礭Τ٤ƤΥޥʤ
ޤ

ʤΤǡɬ׽ʬǤȡϹͤޤ

> ĤθϣߣǤ飵ߣڤФƹͤ뤳ȤǤޤ
> ξ¦飲ޥĤȤäΣߣȹͤ뤳Ȥޤ̤Ʊ
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⡢餫Ȼפޤ
Ǥ礦 ?
109ʶ 7:47:05 43784
Mr.ǥ
錄ν񤭤#43776ˤФɤޤƤޤ

#43779ˡǯԤ#43781
(a,b,c)γ(a,b)Фƾ˹礦㤬̤ꤺĤ뤫ˡǤ͡ޤäͤƤ⤤ʤäˡٶˤʤޤ
(Τ˵Ūʷ׻ǤߡΤ褦ǤͭǤ͡

Jޥޤ#43778ˤ
Ǥβˡ˶ᤤˡȻפޤ錄έ++η64̤ޤȤơʣʬȤ줿Ȥȡ
錄έJޥޤ(2)(3)ȤʤäƤȤۤʤȤǤ͡

⡼ޥ󤵤#43782
12=2*2*3 2Ĥޤ3ĤΤΤѤʬơ줾ξˤĤƲ̤ꤺĹͤ뤫ȤΤǤ͡
ǼǤʻ⤽Τ褦ʤȤͤϤ᤿ΤǤʬʤ٤ʤꤽ˻פơޤ

ߤʤ󤢤꤬Ȥޤ礤˻ͤˤʤޤ
uchinyan#43777ǽ񤫤줿褦
ֳΤ˥åȲ򤱤ˤʤפ褦꤫⤷ޤ͡
109ʶ 10:59:19 43785
uchinyan
#43784
ܡʥꤵ

ʤ뤴ո򤢤꤬Ȥޤ

󡼤ȡ­ݤʤΤǡϿʤäΤǤ

Ǥϡ#43736ǡ
䤷󤳤ۤɤ 3 ܿξʤФʤʤΤǡϡ
1, 4, 7, 22, 25, 28, 43, 46, 49
˹ʤޤƤ¾оξޤºݤ˼¸ǽʤΤưפʬޤ
ȡǸˤäȤǤ¸ǽ˿Ƥޤ
ϡޤǤʤºݤˤäȤäƤߤдñ˼㤬Τǡ餫ȻפäǤ
㤨С졣¾ƱͤǤ
أ££
ţãããģģ
ţƣƣƣǣǣ
ţȣȣȣɣɣ
ʣˣ̣ͣΣϣ
ʣˣ̣ͣΣϣ
ʣˣ̣ͣΣϣ
ǽϸڤޤǤʤʡȤפäΤǤ˲ʤΤⵤΤǰޤ

ܡʥǤϡ#43751ǡ
䢢 3 dzä 0 ;롡ݡݡݡף


䤵ˡϡƥפ΢ФˤʤäƤĤмºݤ˼¸ǽǤ
ȡϤꡤǸˤäȤǤ¸ǽ˿Ƥޤ
⡤ޤǤʤºݤˤäȤäƤߤдñ˼㤬Τǡ餫ȻפäǤ
㤨С졣¾ƱͤǤ
ǣ£££ãã
ǣģģģأ
ǣƣƣƣ
ȣȣȣɣɣɣ
ʣˣ̣ͣΣϣ
ʣˣ̣ͣΣϣ
ʣˣ̣ͣΣϣ
⡤ǽϸڤޤǤʤʡȤפäΤǤ˲ʤΤϥޥȻפޤ


£££ãã
ģģģأ
ƣƣƣǣǣǣ
ȣȣȣɣɣɣ
ʣˣ̣ͣΣϣ
ʣˣ̣ͣΣϣ
ʣˣ̣ͣΣϣ
ϡX = 13 = 2ǻ䤬ǿ줿Ȥϰ㤤ޤ
­ǿޤǤ
оޤ;ξ֥ף Xפ X ȢˤĤơʤȤŪˤϲڤƤޤ
= X Ȥ X 2 * 2 ˼СּºݤˤäƤߤפȤǼ㤬롤Ȥ
嵭Ρ֡פǰѤʸǤϸäƤĤǤ

䤬ͤˡȤСǤϤʤǤ礦 ?
ɤϡʤȻפޤ
䤬ּºݤˤäƤߤСפȸΤ˿޼Ф褫äȤȤˤʤꤽǤ͡

ȤǡAnalytic CombinatoricsŪȤ߹碌ȤǤΤʡȤäơ
7 * 7 Ǥ 3 Ĥξ硤(0,0), (3,0), (6,0), (0,3), (6,3), (0,6), (3,6), (6,6) 8 ĤĤʤ
ȤǤʤΤǤ礦
򤷤ƾͤƤϤߤΤǤ褯ʬäƤʤȤ⤢ꡤ(3,3) ԲĤˤʤäǤޤޤ
ɤʤǤ礦
ͥνȡ 1010ڡ 13:39:55 43786
uchinyan
#43783#43785
Mr.ǥ

ܤ򤢤꤬Ȥޤ

⤤ĤͤΤǤɤ⥹åȤˡ񤭤ޤǤ
ǡ֤Ϥޤñʲˡ񤤤Ƥޤ¿ʬᤤ󤿤Ʊʡ

ĤΥνܤABCA <= B <= CȤCBA ν˷ƾȽꤷޤ
ΤȤA < B < C ʤ 6 ̤ꡤA = B < C A < B = C ʤ 3 ̤ꡤA = B = C ʤ 1 ̤ꡤդ­夲ޤ
ܤ˾ʬ񤭤ѤʤΤǤñʤΤǤۤȤƬǤǤƤޤ
C = 10
C = 20
C = 33
C = 415 + 3 = 18
C = 56
C = 69 + 6 + 21 + 12 + 16 = 64
ס91 ̤

⡼ޥ󤵤Τä̤ꡤ6^3 - 5^3 = 91Ȥ3H12 = 14C2 = 91ʤΤǡ
ʤʡȻפäΤΡʬ餺
ͥνȡ 109ʶ 13:09:37 MAIL:uchi@sco.bekkoame.ne.jp 43787
ǯ
#43784ܡʥꤵ󡪤Ǥ򤪤ƤޤäȽ꤫Ƥޤ
109ʶ 20:16:42 43788
Mr.ǥ
#43787 uchinyan
ͭ񤦤ޤ
οʬषƤȤˤꥴ룱˰󤻡
ƻˡ׻ƤΤǤ͡ǼǤ
ʷɡC15έˡC=6έ˳뤳ȤˤʤΤǤ͡
109ʶ 22:26:53 43790
ܡʥ
ѥ˽ФƤᡢֻ٤ޤ

ǯԤ #43788

ΩƤʤ顢줷¤Ǥ

uchinyan #43786

ۣʵҤˤ򤬲򤱤褦ǡ줷Ǥ

ʤ֤ˤĤƤϡuchinyan ˤǤϤʤ
¸ǽ򼨤ƤʤؤεǤ
⡢Ƚ񤯤٤

ּפɤȤΤǤ¾ͤˤȤäɬ
줬ּפǤȤϸ¤ޤ

ޤּפǤȽǤ⡢ͤˤäƥޥ
ޥäꤷޤơʬȤϰ㤦ܤ
饦äꤷޤ

ʤΤǡǤСּפȽǤˤä
ĺäΤǤ

Analytic Combinatorics ηǤޤȤ
פΤǤޤƤޤ󡣻Τꤿ
Ǥ

뤤ΤǤ̤餹ȡ

(x 0 (mod 3) AND y 0 (mod 6)) OR (x 0 (mod 6) AND y 0 (mod 3))

ˤʤΤǡ1 6 躬ΤǤϤʤǤޤ

ޤ1x1 3 Ĥǹϡͤ
6 ġ濴ȤСü 4
꤫顢2 ս֤Ȥ٤ƤηɽǤޤ

ʤΤǡʤְäƤȤϻפޤ

ơθĿͤȡ ܤȤʤؿ f ϡ
濴κɸ a֤Ƥ t Ȥ
Ŀ c 3 ѿˤ¿༰ˤʤ뤫Ȼפޤ

Ū¿༰ηפ⤫Ӥޤ
ɤʤˡƳФߤȻפäƤޤ
1014ʿ 8:40:45 43791