nobu
ܥ-ǤУϣˡ
Υե߻äɶå̵⡣
68ڡ 0:08:38 27558
ޥ
פäԿӤ԰¤Ǥ...Ūʴְ㤤򤷤Ƥ뤫...伫ʬ
PowerBook G4 68ڡ 0:10:36 MAIL:masaru-y@sansu.org HomePage:27559
ڼ
ʤȻפޤ
^ᣳ^򤦤äꤷơäƤޤޤ
͡ 68ڡ 0:12:54 MAIL:iida@ae.keio.ac.jp 27560
Taro
#27559
ץĴ٤ƤߤޤְäƤϤʤ褦Ǥ
68ڡ 0:13:50 27561
ޥ
ۥáǿʤǤޤ(^^;

ʣߣߣˡࣲܣᣳ

Ȥ׻ꤷƤޤ
PowerBook G4 68ڡ 0:15:17 MAIL:masaru-y@sansu.org HomePage:27562
ޤ夢դޤ
Фϡ

ϣǰΤֻǫĺޤƤ꤬Ȥޤ
ޤʾǤˤʤΤǡ˿ƶᴶ襤ơ޸ߤ˻äƤޤ
ξڤƤ鿽夲ޤ
͡ 68ڡ 0:25:22 MAIL:top-amateur@u01.gate01.com 27563
ѥ
504x504=2^6x7^2x3^4
ʥ+ˤȡʥ-ˤ϶Ǥ뤳Ȥͤȡ
{(6-1)x(2+1)x(4+1)-1}/2 +1=38
˿ꡡ 68ڡ 0:25:46 MAIL:dr-yasu@nifty.com 27564
ߤ
λ椫꾮ڤȤƱȤʤǤ
⹻ΤȤñǤä褦ʡġλǤ
κ餤äΤǡŪŬˤäۤȤ
Ĥʤäʡ⤷ƤʤȤ´ʴˡ
68ڡ 0:31:23 27565
ѥ
äƤޤޤʾСˡ
{(6-1)x(2+1)x(4+1)-1}/2 +1=38
Ȥ2dz뤳ȤʬäƤΤǤ(6-1)x(2+1)x(4+1)ʬϴФꡪ
504x504 at =0 ξ礬ޤ餹Ǥǡǰʬ򲿲ľꡢФ餯ͤǤޤޤ
Ѥ餺ɽŪultra hardʥޤǤ
˿ꡡ 68ڡ 0:55:24 MAIL:dr-yasu@nifty.com 27566
Ȥ
ե߿ߤޤϹԤäȤʤΤǤε
ɤʽ꤫ԤȻפäΤǤ

377󤫤λäʤΤǻ¤ΤDzǤ򤤤ƻäȻפޤ
˭ԡ 68ڡ 1:43:20 MAIL:fttnm528@ybb.ne.jp 27567
ʤ
#27562 ޥ뤵

ʣߣߣݣˡࣲܣᣳ
Ʊ׻ˤʤޤ

ܥᣲᡤݥᣲȽ񤯤ȡդϡ
ߣᣲߣʤȡʣᡤˤξο


ǡߣᣲߣߣʤΤǡ
ϡʣܣˡߡʣܣˡߡʣܣˡ᣷
ΤΤȾʬΡʣݣˡࣲܣᣳ
ʤüϡᣲξʤΤŬ

# Ѥߡʣᢪʤɡ
68ڡ 12:22:15 MAIL:naka@sansu.org 27568
uchinyan
ϤϤ褦ޤ
ϡñʥϥʤǤĤޤʤߥϢȯơųݤ줿ʡˤϤޤäƤޤޤ (^^;

ܥ ݥ ϡ504 * 504 = 2^6 * 3^4 * 7^2 ʤΤǡθĿФ櫓Ǥ
ܥ ݥ ¤ȺǤʤȤʤΤǡ
ܥ ݥ ѤǤ뤳ȤͤȡξȤǤʤФʤޤ
ǡξ˺ǽ 2 ĤۤäƤơĤ 2^4 * 3^4 * 7^2 θĿͤɬפޤ
ޤ˰äޤ ^^;
ϡ(4 + 1) * (4 + 1) * (2 + 1) = 5 * 5 * 3 = 75 Ǥ
>= 0 ʤΤǡܥ >= ݥ ȡ = 0 ܥ = ݥ դʤФʤޤ
ˡ˰äޤ ^^;
ɡΤϡ(75 + 1)/2 = 76/2 = 38 ̤ ˤʤޤ

Ρʤβˡȡ§ƱͤǤ͡
ͥνȡ 68ڡ 8:58:31 MAIL:uchi@sco.bekkoame.ne.jp 27569
⡼ޥ
빽Ǻߤޤ

a*b=2^6*3^4*7^2
a,b ϡʤΤǡa'*b'=2^4*3^4*7^2
2 Ȥ߹碌ϡ0-4,1-3,2-2
3 Ȥ߹碌ϡ0-4,1-3,2-2
7 Ȥ߹碌ϡ0-2,1-1
2*(2^2+1)(2+1)+1*3*(2+1)=39
a'=b'ΤȤơ39-1=38

줪Ǥ͡

ˤϡ
2*2^2*(2+1)+2*1*(2+1)+1*2*(2+1)+1*1*2
=24+6+6+2
=38
Ǥ͡Ǥ䤳
ߤʤٶˤʤޤOrZ
ɤ⡢μ϶ʡ(^^;

68ڡ 13:01:13 MAIL:kennji72001@yahoo.co.jp 27570
ϥ饮㡼ƥ
Ϥ褦ޤߤĤ֤Mathematica
׻ޤο1ޤǤǤȤǧڤǤ
̶彣 68ڡ 10:46:29 HomePage:ĩ27571
ʤ
#27555,#27556

ºݤˤäƤߤȡN=4k,N=4k+1 ʤ餹٤ƤǤǤ
η̤θǤN= 5 : 1, 3, 5, 2, 4ϡ
Ƥο礭顢5-1, 4-3, 3-5, 2-2, 1-4Ȥ̣Ǥ

N= 4 : 1, 3, 4, 2
N= 5 : 1, 3, 5, 2, 4
N= 8 : 1, 2, 4, 5, 8, 6, 3, 7
N= 9 : 1, 2, 3, 6, 7, 5, 8, 9, 4
N=12 : 1, 2, 3, 4, 7, 9, 6, 8, 10, 11, 12, 5
N=13 : 1, 2, 3, 4, 6, 8, 9, 7, 10, 11, 12, 13, 5
ά
N=28 : 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 16, 18, 19, 14, 20, 17, 22, 13, 24, 21, 26, 23, 28, 25, 12, 27
N=29 : 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 17, 18, 16, 20, 22, 19, 15, 21, 12, 23, 24, 25, 26, 27, 28, 29, 14
68ڡ 12:49:41 MAIL:naka@sansu.org 27572
uchinyan
Ǽġɤߤޤ
ϡΤ褦ˡ֤ʡˤϤޤäƤޤä׿ͤ⤤褦Ǥ
ϤꡢŪˤ񤷤ʤΤǡä򤽤äϤʤ褦Ǥ

ʤ#27571
䤷ߤĤ֤Mathematica ׻ޤο1ޤǤǤȤǧڤǤ
ץϡʥ֤ˡȥť롼פǤäꤹȡ
롼פϰϻ꼡ǤϡʤʤλʤʤäƤޤäꤷޤ ^^;
ͤޤǤˡפʥ١åǤʤСŪ᤯λޤ
= a, = b Ȥơa^2 = b^2 + 504^2 ȡa - b >= 2 ܤơb θϰϤ򤢤餫ʤäƤޤ
ޤǤ⤴ͤǤMobile Pentium IV 2.2 GHz 496 MB餤ΥΡPCȤäƤޤ

REM ˥󥸣
LET t = TIME
LET cnt = 0
LET m = 504 * 504
FOR b = 0 TO (m/2 - 2)/2
LET a = SQR(b * b + m)
IF a = INT(a) THEN
LET cnt = cnt + 1
PRINT cnt; ""; a; ""; b; "ܥ"; a + b; "ݥ"; a - b
END IF
NEXT b
REM PRINT cnt
PRINT TIME - t; " ޤ"
END

Ϸ

1 504 0 ܥ 504 ݥ 504
2 510 78 ܥ 588 ݥ 432
3 520 128 ܥ 648 ݥ 392
4 525 147 ܥ 672 ݥ 378
5 546 210 ܥ 756 ݥ 336
6 554 230 ܥ 784 ݥ 324
7 579 285 ܥ 864 ݥ 294
8 585 297 ܥ 882 ݥ 288
9 630 378 ܥ 1008 ݥ 252
10 679 455 ܥ 1134 ݥ 224
11 696 480 ܥ 1176 ݥ 216
12 746 550 ܥ 1296 ݥ 196
13 840 672 ܥ 1512 ݥ 168
14 865 703 ܥ 1568 ݥ 162
15 954 810 ܥ 1764 ݥ 144
16 1071 945 ܥ 2016 ݥ 126
17 1190 1078 ܥ 2268 ݥ 112
18 1230 1122 ܥ 2352 ݥ 108
19 1345 1247 ܥ 2592 ݥ 98
20 1371 1275 ܥ 2646 ݥ 96
21 1554 1470 ܥ 3024 ݥ 84
22 1800 1728 ܥ 3528 ݥ 72
23 2296 2240 ܥ 4536 ݥ 56
24 2379 2325 ܥ 4704 ݥ 54
25 2670 2622 ܥ 5292 ݥ 48
26 3045 3003 ܥ 6048 ݥ 42
27 3546 3510 ܥ 7056 ݥ 36
28 3985 3953 ܥ 7938 ݥ 32
29 4550 4522 ܥ 9072 ݥ 28
30 5304 5280 ܥ 10584 ݥ 24
31 7065 7047 ܥ 14112 ݥ 18
32 7946 7930 ܥ 15876 ݥ 16
33 9079 9065 ܥ 18144 ݥ 14
34 10590 10578 ܥ 21168 ݥ 12
35 15880 15872 ܥ 31752 ݥ 8
36 21171 21165 ܥ 42336 ݥ 6
37 31754 31750 ܥ 63504 ݥ 4
38 63505 63503 ܥ 127008 ݥ 2
.58 ޤ

ĿĴ٤ʤС

38
.14 ޤ

Ȥʤޤ
ͥνȡ 68ڡ 13:13:29 MAIL:uchi@sco.bekkoame.ne.jp 27573
uchinyan
#27572
#27555,#27556
ºݤˤäƤߤȡN=4k,N=4k+1 ʤ餹٤ƤǤǤ
աࡢ̤ȤơִפΥåɬ׽ʬˤʤäƤȤȤǤ͡
ǤΤʡ
ͥνȡ 68ڡ 13:22:01 MAIL:uchi@sco.bekkoame.ne.jp 27574
⡼ޥ
#27572
ʤء
Ǥ͡äѤץǤ͡
ʴʤ餹٤ƤǤʵ⤷ޤ
ξäƤǤΤǤ礦
68ڡ 13:48:53 MAIL:kennji72001@yahoo.co.jp 27575

ᥢܥ¡ᥢݥ Ȥȡ
ߣ¡2^63^47^2ܣ¡ᣲߥ
줫顢ȣ¤ϤȤ˶ʬΤǡ2^63^47^2
2ĤζѤˤɤȤˤʤޤ

ǡ褺6Ĥ2򡢤ɤˤ1Ĥ褦Ĥʬơ
Ĥ4Ĥ32Ĥ7򿶤ʬޤ

21Ĥ5Ĥʬ
4Ĥ3ȡ2Ĥ7ɤˤդ뤫ǡ5315̤
22Ĥ4Ĥʬ
4Ĥ3ȡ2Ĥ7ɤˤդ뤫ǡ5315̤
23Ĥ3Ĥʬ
㤨С31Ĥ72ˤäĤΤȡ
33Ĥ70ˤäĤΤƱˤʤ뤳Ȥ
դơ8̤

ɡ1515838̤ꡡˤʤޤ
68ڡ 14:46:23 27576
⡼ޥ
#27576 󤵤βˡϡ
錄ƱץǤ
錄Τꤺäȥޡȡ(^^)
68ڡ 16:03:00 MAIL:kennji72001@yahoo.co.jp 27577
uchinyan
#27572 #27556
ʤ󡢥⡼ޥ󤵤ء
äȡ֤졩פäȻפäΤǤ

N = 8 ξ硢

ʤβN= 8 : 1, 2, 4, 5, 8, 6, 3, 7Ĥޤꡢ
ɽ8 7 6 5 4 3 2 1
΢1 2 4 5 8 6 3 7
7 5 2 0 4 3 1 6

⡼ޥ󤵤β1-8,1-7,3-8,2-6,2-5,3-5,6-7,4-4Ĥޤꡢ
ɽ8 7 6 5 4 3 2 1
΢1 6 2 3 4 8 5 7
7 1 4 2 0 5 3 6

Ĥϡ 0 ˤʤȤ㤦ۤʤäƤꡢϡˡǤϤʤΤǤ͡
ʤβϡץåΤʡȻפäΤǤ㤦ΤǤ礦
ʤȡ򤬤Ĥ뤫⡢ˤʤäƤꡥ
ͥνȡ 68ڡ 16:24:10 MAIL:uchi@sco.bekkoame.ne.jp 27578
kashi
βοϡ

N=4 4
N=5 4
N=8 32
N=9 96
N=12 992
N=13 2512
N=16 50512

Ȥʤꤿ󤢤褦Ǥ
(ɽ=1NȤ΢ο᤿Τǡ¼ŪˤȾʬǤ礦)

餷ƲϤäȤꤽʵϤǤ
񤷤Ǥͤ
68ڡ 16:36:39 27579
uchinyan
#27579
kashi󡢾󤢤꤬Ȥޤ
ʤˤΤǤ¿ʬʤϡĤĵ󤲤ΤǤ礦͡
䤳餷ƲϤäȤꤽʵϤǤ
Τˡ
񤷤Ǥͤ
äȵˤʤäơο󥵥ȤĴ٤Ƥߤ顢A075866Ǥޤ

http://www.research.att.com/~njas/sequences/A075866
A075866 Number of permutations s of {1,2,...,n} such that |s(i)-i| for i=1,2,...,n are all distinct.
A075866 {1,2,...,n} Ρi=1,2,...,n Ф |s(i)-i| ٤ưۤʤ s θĿ

ΥꤽΤޤޤǤ͡
ʤΤޤǤȤϡǤ⡢ޤ꿷Ϥʤʤ
ͥνȡ 68ڡ 16:57:52 MAIL:uchi@sco.bekkoame.ne.jp 27580
⡼ޥ
#27579
kashiء
οϤɤäƵ줿ΤǤ
ˡäƤȤϾ˲¸ߤäƸޤ͡
68ڡ 17:11:03 MAIL:kennji72001@yahoo.co.jp 27581
kashi
#27580
uchinyan󡢤򤤥ȤǤ͡󤢤꤬Ȥޤ

#27581
⡼ޥ󤵤󡢴ñʥץõǤ
68ڡ 17:49:36 27582
ʤ
>¿ʬʤϡĤĵ󤲤ΤǤ礦͡
ΤȤǤ
οȯŪ뤳ȤʬäΤǡ㤬Ĥä
ΣΤĴ٤뤳Ȥˤޤ

¸ߤξǤȤ顢ǼŪˡͭϤΤ褦ʵޤ
N=k β򤫤 N=k+4 βƳȯФ褤櫓Ǥ
⡢ʲ򤬤üʰʣˤǤ⼨ФΤǡ
̮ϤޤꤽʤΤǤȤϤǤϤޤ
68ڡ 18:20:28 MAIL:naka@sansu.org 27583

βϡ˸ŪǤ
ޤ򸫤504ǰʬ2^3*3^2*7Ȥȥ¤ȺѤ504Σ(254016)顢2^6*3^4*7^2ȤʤꡢοϣĤꡢ򣲤ĤοѤ254016ˤʤ褦ˣȤȥᥤ504񤭽Ф(1,254016)(2,127008)(3,84672)(432,588)(441,576)(448,567)Ȥ褦ˡΣݥǸ夬ܥȤ롣
ĤޤꡢϢΩ饢ϣ¤ȾʬȤʤꡢ
:ݥ1,ܥ254016 127008.5Ǿﳰ
ݥ2,ܥ127008 63505 63503ȤϾ
ĤޤꡢȤǤΤ(15)ϾﳰȤʤꡢ52-15=37ȥᥤ504Σ̤ȵ᤿
68ڡ 23:11:23 27584
ERĹ
()X(+)=504X504

504=2^3X3^2X7^1
504X504=2^6X3^4X7^2

顢()504 ǡ(+)ˤʤȹ礻ǹͤޤ
68ڡ 23:27:26 27585
ߤγ
ƻäޤǤʤΤǤˡǤ
ߥݥߥ504504ˤʤޤѤκǹͤ
ء٤¤٤ФοεѤޤ
;ȾοȾξ֤ޤǤ
ΰξѤ504504463504ǡ
ġĹȤ߹碌(163504)(252252)
ޤǤǤ63504ο75Ĥäơ252252Τ
Υڥͤ(751)238ˤʤޤ

68ڡ 23:50:03 27586
fumio
񤷤ä
69ʶ 7:31:59 27587
uchinyan
#27586
Ūˤϡͤ¾γƱˡʤΤǤŪªƤ餷ƤʡȻפޤ
ʤ#27565ƱˡʤΤʡȡƻפޤ

ϡŻι֤˹ͤȤʤͤƤߤΤΡʹͤ٤˻ꡢȤǡŸʤ
İ뤿ˡ⽽ʥ١åǥץȤǤߤޤ
ʥ֤˽ǤФ٤ƥå륢르ꥺʤΤǡN = 12 դǥ֥åפΤ褦ǤޤǤϡƸǤƤ褦Ǥ
顢ǼŪ˹ʤɤλˤʤ롢ε§뤫ɤ
ͥνȡ 69ʶ 17:39:02 MAIL:uchi@sco.bekkoame.ne.jp 27588
ޥ
޷ŪȸСϡж x^2-y^2=504^2ˤʻοפȤۤƱǤ͡
PowerBook G4 69ʶ 19:11:05 MAIL:masaru-y@sansu.org HomePage:27589
uchinyan
#27589
޷ŪȸСϡж x^2-y^2=504^2ˤʻοפȤۤƱǤ͡
ʤۤɡΤˡȡ񤷤˸ޤ ^^;
ʤߤˡ504^2 + y^2 = x^2 ȤСԥ饹롢롢ˤʤޤ͡
ͥνȡ 610ڡ 13:32:23 MAIL:uchi@sco.bekkoame.ne.jp 27590

ǯ֤˥󥸤ޤ^^
ˡϳƱͤǤ
ߣᣲȤƤϤޤ><
夫ľƤޤ( TT)
610ڡ 15:33:35 27591