¥´¥ó¤È¤â
¿ô¼°½èÍý¤Ç¥â¥íľ¤Ç¤·¤¿¡£

(C1) 666666666666666666666666666666*666666666666666666666666666668;
(D1) 444444444444444444444444444444 888888888888888888888888888888
(C2) 4*30+8*30;
(D2) 360
Ë­Àî»Ô¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 0:05:49¡¡¡¡ MAIL:fttnm528@ybb.ne.jp ¡¡¡¡27461
µÈÀî¡¡¥Þ¥µ¥ë
¤Á¤ç¤Ã¤È´Êñ¤¹¤®¤Þ¤·¤¿...¡£m(__)m
PowerBook G4¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 0:08:15¡¡¡¡ MAIL:masaru-y@san¡¡su.org HomePage:»»¥Á¥ã¥ì¡¡¡¡27462
LiE
666*668=444888¤Çµ¤¤¬¤Ä¤­¤Þ¤·¤¿¡°¡°
4*30=120
8*30=240
120+240=360
µþÅÔ»ÔÆâ¤ÎÅļˡ¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 0:08:25¡¡¡¡ MAIL:njswg145@ybb.ne.jp ¡¡¡¡27463
fumio
¤³¤ó¤Ð¤ó¤Ï¡£
¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 0:08:46¡¡¡¡ ¡¡¡¡27464
¥«¥¤¥È
¥¢*¥¤¤¸¤ã¤Ê¤¯¤Æ¥¤*¥¢¤ò¤¹¤ë¤È³Ú¤Ã¤Æ¤³¤È¤Ç¤¤¤¤¤Î¤«¤Ê¡Ä
¤Á¤ç¤Ã¤ÈÇï»ÒÈ´¤±¤·¤Þ¤·¤¿¡¥
¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 0:09:37¡¡¡¡ ¡¡¡¡27465
¾Ã¤·¥´¥à¥Ñ¥È¥í¡¼¥ë
6*8=48
66*68=4488
666*668=444888
¤«¤éÎà¿ä¤·¤Þ¤·¤¿
¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 0:10:00¡¡¡¡ ¡¡¡¡27466
DrK
¤³¤ì¤Ï6¡¦¡¦¡¦¡¦¡¦6¡ß6¡¦¡¦¡¦¡¦¡¦8=2¡¦¡¦¡¦¡¦¡¦2¡ß3¡ß6¡¦¡¦¡¦¡¦¡¦8¤ò¹Í¤¨¤ì¤Ð·×»»¤¬³Ú¤Ç¤¹
¤³¤³¤«¤é
2¡¦¡¦¡¦¡¦¡¦2¡ß2000000000000000000000000000004¤È¤Ê¤ê¡¢4¡¦¡¦¡¦¡¦¡¦48¡¦¡¦¡¦¡¦¡¦8¤È¤Ê¤ê¤Þ¤¹
¤³¤³¤«¤é4¡ß30+8¡ß30=360¤¬Åú¤¨
¤Ç¤â»ä¤Ï²¿¸Î¤«240¤òÁ÷¤Ã¤Æ¤·¤Þ¤¤¤Þ¤·¤¿¡£
¤½¤Î¤¿¤á»þ´Ö¤ò¥í¥¹¤¹¤ë·ë²Ì¤È¤Ê¤ê¤Þ¤·¤¿¡¢
2/3¡ß2/3=4/9¤¬»È¤¨¤Ê¤¤¤«¤È¹Í¤¨¤Æ¤¤¤Æ»×¤¤¤Ä¤­¤Þ¤·¤¿
º£ÅÙ¤³¤½ÃϾå¤Î³Ú±à¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 0:11:28¡¡¡¡ MAIL:satoka@star.odn.ne.jp ¡¡¡¡27467
¿ô³Ú¼Ô
¼ê·×»»¤Ç¤¹
66¡¦¡¦¡¦668¡ß6=400¡¦¡¦¡¦008
£±·å¤º¤Ä¤º¤é¤·¤Ê¤¬¤é¡ÊƬ¤ÎÃæ¤Ç)30¸Äʤ٤ޤ·¤¿¡£
²£ÉÍ¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 0:11:59¡¡¡¡ MAIL:iida@ae.keio.ac.jp ¡¡¡¡27468
¤ª¤«¤Ò¤ÇÇî»Î
¤¿¤Þ¤Ë¤Ï¡¢¤³¤ó¤Ê¤Î¤¬¤¢¤ë¤È¥Û¥Ã¤È¤·¤Þ¤¹
£³£³¡¦¡¦£³£³¡ß£³£³¡¦¡¦£³£´¤ä
£¶£¶¡¦¡¦£¶£¶¡ß£¶£¶¡¦¡¦£¶£·¤Ê¤É¤âƱ¤¸¤Ç¤¹¤Í
¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 0:15:10¡¡¡¡ ¡¡¡¡27469
¤Á¤ã¡¼¤ß¡¼
#27468 ¤Ê¤ë¤Û¤É¡¤¤½¤ì¤À¤±¤Î¤³¤È¤«¡£

n ¸Ä¤Î¾ì¹ç¡¤ÀÑ = (666¡Ä67)^2-1 = (2*10^n +1)^2 /9 -1
= 4*(10^{2n}-1)/9 + 4*(10^n -1)/9
¤ÈÊÑ·Á¤·¤Æ¤ä¤ê¤Þ¤·¤¿¡£
ÅìµþÅÔÌܹõ¶è¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 0:21:08¡¡¡¡ MAIL:ojamaru@amber.plala.or.jp ¡¡¡¡27471
¾Ã¤·¥´¥à¥Ñ¥È¥í¡¼¥ë
>DrK
¤¹¤´¤¤¡ª
¤¢¤ó¤¿Å·ºÍ¤Á¤ã¤¦¤«¡©
¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 0:25:10¡¡¡¡ ¡¡¡¡27472
ERÉôĹ
#27466¤ÈƱ¤¸²òË¡¤Ç¤¹m(__)m
¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 0:52:56¡¡¡¡ ¡¡¡¡27473
¥Î¥Ü¥±¥¤¥ó
¥Þ¥µ¥ë¤µ¤ó¡¢¤Þ¤À¤Þ¤À¡¢¥Í¥¿Àڤ줷¤Æ¤Þ¤»¤ó¤Í¡£
¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 2:22:24¡¡¡¡ ¡¡¡¡27474
¥Ï¥é¥®¥ã¡¼¥Æ¥¤
¤ª¤Ï¤è¤¦¤´¤¶¤¤¤Þ¤¹¡£

Mathematica¤Ç¥¢¤òa¡¢¥¤¤òb¤È¤·¤Æ

Total[IntegerDigits[a*b]]

¤È¤·¤¿¤éÅú¤¨¤¬½Ð¤Þ¤¹¡£¤¤¤í¤¤¤í´Ø¿ô¤¬¤¢¤ë¤â¤Î¤Ç¤¹¡£
Ë̶彣¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 7:14:13¡¡¡¡ HomePage:¿®¹æ½èÍý¤ËÄ©Àï¡¡¡¡27475
¥¹¥â¡¼¥¯¥Þ¥ó
Ʊ¤¸¤¯Îà¿ä¤Ç¡£¡£¡£(^^)
¶â¸÷¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 7:34:02¡¡¡¡ MAIL:kennji72001@yahoo.co.jp ¡¡¡¡27476
uchinyan
¤Ï¤¤¡¢¤ª¤Ï¤è¤¦¤´¤¶¤¤¤Þ¤¹¡£¤³¤Î»þ´Ö¤Ê¤Î¤Ç¡¢Îã¤Ë¤è¤Ã¤Æ¡¢°Å»»¤Ç¤¹ ^^/
66..(30¸Ä)..66 * 66..(29¸Ä)..68
= 4 * 33..(30¸Ä)..33 * 33..(29¸Ä)..34
= 4 * 33..(29¸Ä)..34 * 3 * 11..(30¸Ä)..11
= 4 * 100..(29¸Ä)..02 * 11..(30¸Ä)..11
= 4 * 11..(30¸Ä)..1122..(30¸Ä)..22
= 44..(30¸Ä)..4488..(30¸Ä)..88
¤Ê¤Î¤Ç¡¢Åú¤¨¤Ï¡¢
(4 + 8) * 30 = 360
¥Í¥³¤Î½»¤à²È¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 8:19:01¡¡¡¡ MAIL:uchi@sco.bekkoame.ne.jp ¡¡¡¡27477
uchinyan
·Ç¼¨ÈÄÆɤߤޤ·¤¿¡£¤¬¡¢½êÁ§·×»»¤À¤±¤Ê¤Î¤Ç¡¢¤¢¤Þ¤êÌÌÇò¤½¤¦¤ÊÏäϤʤ¤¤Ç¤¹¤Í¤§¡£
»ä¤Î¾ì¹ç¤Ï¡¢66..66 ¤«¤é¡¢2/3 = 0.666..., 1/3 = 0.333..., 3 * 1/3 = 1 = 0.999... ¤À¤Ê¤¡¡¢¤ÈÏ¢ÁÛ¤µ¤ì¡¢
66...66 = 2 * 33...33, 66...68 = 2 * 33...34, 33...33 * 3 = 99...99, 33...34 * 3 = 100...02 ¤¸¤ã¤¡¤Ê¤¤¤«¡¢
¤È¤¤¤¦´¶¤¸¤Ç¡¢¸å¤Ï#27477¤ÎÄ̤ê¤Ç¤·¤¿ ^^;
¥Í¥³¤Î½»¤à²È¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 9:13:08¡¡¡¡ MAIL:uchi@sco.bekkoame.ne.jp ¡¡¡¡27478
¥â¥Î¥ª¥¸ÆóÅùʼ
¤¤¤Ä¤â»»¥Á¥ã¥ì¤ÎÌäÂê¤Ï¤Ç¤­¤Ê¤¤¤Î¤Ëº£²ó¤Ï£³Ê¬¤Ç¤Ç¤­¤Þ¤·¤¿¡ù
¾Ã¤·¥´¥à¥Ñ¥È¥í¡¼¥ë¤µ¤ó¤ÈƱ¤¸Îà¿ä¤Ç¤ä¤ê¤Þ¤·¤¿
¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 10:28:40¡¡¡¡ MAIL:nagamikoko1000@gmail.com ¡¡¡¡27479
¤Þ¤ë¥±¥ó
µ×¤·¤Ö¤ê¤Î¥ï¥ó¥é¥¤¥Ê¡¼
ruby -e 'p eval((("6"*30).to_i * (("6"*30).to_i+2)).to_s.split("").join("+"))'
¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 11:42:26¡¡¡¡ MAIL:take4310@mobile.email.ne.jp HomePage:¤Þ¤ë¥±¥ó¤ÎÉô²°¡¡¡¡27480
¥¹¥â¡¼¥¯¥Þ¥ó
¤Á¤Ê¤ß¤Ë¡¢
(66...66)^2 ¤Î¾ì¹ç¤Ï¡¢66...66*2=133...32 ¤Ê¤Î¤Ç¡¢1+3*29+2=3*30=90 ¤«¤é¡¢360-90=270 ¤Èʬ¤«¤ê¤Þ¤¹¤Í¡£
¶â¸÷¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 13:00:06¡¡¡¡ MAIL:kennji72001@yahoo.co.jp ¡¡¡¡27481
Â粬¡¡ÉÒ¹¬
£¶¡ß£¸¡á£´£¸
£¶£¶¡ß£¶£¸¡á£´£´£¸£¸
£¶£¶£¶¡ß£¶£¶£¸¡á£´£´£´£¸£¸£¸
¤«¤±¤ë¿ô¤Î·å¿ô¤ÈÅú¤¨¤Î£´¤È£¸¤Î¿ô¤¬Æ±¤¸¤ÈͽÁÛ¡Ê¡°¡°¡Ë
¤è¤Ã¤Æ¡¡¡¡¡Ê£´+£¸¡Ë¡ß£³£°¡á£³£¶£°
º£²ó¤Ï¤³¤ó¤Ê´¶¤¸¤Ç¹Í¤¨¤Þ¤·¤¿¡Ê¡°¡°¡Ë¾¤ÎÊý¤Î²ò¤­Êý¤â»²¹Í¤Ë¤µ¤»¤Æ¤â¤é¤¤¤Þ¤¹¡£
ÀÐÀ¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 13:52:26¡¡¡¡ MAIL:toshi009@land.hokuriku.ne.jp ¡¡¡¡27482
ryuta422
6x8=48¢ª12 66x68=4488¢ª24¡¦¡¦¡¦¡¦¡¦¡¡¡¡ 12x30=360¡ÄÅú¤¨
¡¡¡¡ ¢¬¡¡¡¡¡¡¡¡¡¡ ¢¬ ¢¬
¡¡ £±·å¡¡¡¡¡¡¡¡ £²·å¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡£³£°·å
¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 18:59:33¡¡¡¡ ¡¡¡¡27483
ryuta422
¤ä¤¸¤ë¤·¤Î°ÌÃ֤Ȥ«´Ö°ã¤Ã¤Æ¤¤¤ë¤È¤³¤¬¤¢¤ê¤Þ¤·¤¿
¤¹¤¤¤Þ¤»¤ó^^;
¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 19:00:45¡¡¡¡ ¡¡¡¡27484
tapu
µ×¤·¤Ö¤ê¤Ë²ò¤±¤Þ¤·¤¿¡£¤¦¤ì¤·¤¤¤Ç¤¹¡ª
¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 20:09:48¡¡¡¡ ¡¡¡¡27485
¥È¥â¥Ò¥í
¤³¤ó¤Ê¤Ë¤­¤ì¤¤¤Ê¿ô»ú¤Ë¤Ê¤ë¤È¤Ï»×¤¤¤â¤·¤Þ¤»¤ó¤Ç¤·¤¿¡£
̾¸Å²°¡¡¡¡ 5·î25Æü¡ÊÌÚ¡Ë 23:45:32¡¡¡¡ ¡¡¡¡27486
uchinyan
º£²ó(£µ£°£²²ó)¤ÎÌäÂê¤Ï´Êñ¤¹¤®¤¿¤è¤¦¤Ê¤Î¤Ç¡¢º£²ó¤ÎÌäÂ꤫¤é»×¤¤¤Ä¤¤¤¿¡¢¤³¤ó¤ÊÌäÂê¤Ï¤É¤¦¤Ç¤·¤ç¤¦¤«¡©
¤ª²Ë¤ÊÊý¤¬¤¤¤¿¤é¡¢¹Í¤¨¤Æ¤ß¤Æ¤¯¤À¤µ¤¤¡£
¼¡²ó(£µ£°£³²ó)¤ÎÌäÂê¤Ã¤Ý¤¯¡¥¡¥¡¥(^^;

£µ£°£³¤Ë¤¢¤ë¼«Á³¿ô¥¢¤ò¤«¤±¤¿¤é¡¢£¹£¹£¹¡Ä£¹£¹¤Î¤è¤¦¤Ë£¹¤¬Ê¤ּ«Á³¿ô¥¤¤Ë¤Ê¤ë¤³¤È¤¬¤¢¤ë¤Ç¤·¤ç¤¦¤«¡©
¤¢¤ë¾ì¹ç¤Ë¤Ï¡¢¤½¤Î¤è¤¦¤Ê¼«Á³¿ô¥¤¤Î£¹¤Î¸Ä¿ô¤òµá¤á¤Æ¤¯¤À¤µ¤¤¡£
¤¿¤À¤·¡¢¥¤¤¬Ê£¿ô¤¢¤ë¾ì¹ç¤Ë¤Ï¡¢¤½¤Î¤¦¤Á¤Î°ì¤Ä¤Ë¤Ä¤¤¤Æµá¤á¤ì¤Ð¤¤¤¤¤â¤Î¤È¤·¤Þ¤¹¡£
Åú¤¨¤Ï¡¢¤Ê¤¤¾ì¹ç¤Ë¤Ï£°¡¢¤¢¤ë¾ì¹ç¤Ë¤Ï¤½¤Î¥¤¤Î£¹¤Î¸Ä¿ô¤È¤·¤Þ¤¹¡£

¤¤¤­¤Ê¤ê¤À¤ÈÆñ¤·¤¤¤«¤â¤·¤ì¤Þ¤»¤ó¡£
ºÇ½é¤Ë¡¢£³¡¢£·¡¢£±£·ÊÕ¤ê¤Ç¹Í¤¨¤Æ¤ß¤ë¤È¡¢¼ê¤¬¤«¤ê¤¬¸«¤Ä¤«¤ë¤È»×¤¤¤Þ¤¹¡£

¤Ê¤ª¡¢¼Â¤Ï¥Ò¥ó¥È¤¬¡¢·Ç¼¨ÈĤνñ¤­¹þ¤ß¤ÎÃæ¤Ë¤¢¤ê¤Þ¤¹ ^^;
¥Í¥³¤Î½»¤à²È¡¡¡¡ 5·î26Æü¡Ê¶â¡Ë 13:39:04¡¡¡¡ MAIL:uchi@sco.bekkoame.ne.jp ¡¡¡¡27487
¥¹¥â¡¼¥¯¥Þ¥ó
#27487
19^2=361<503<23^2=529 ¤Ç¡¢3~19 ¤Þ¤Ç¤ÎÁÇ¿ô¤Ç³ä¤ì¤Ê¤¤¤Î¤ÇÁÇ¿ô¡£
10^502¢á1 (mod 503)¡¦¡¦¡¦¥Õ¥§¥ë¥Þ¡¼¤Î¾®ÄêÍý¤è¤ê¡£
¤À¤«¤é¡¢9¤Î¸Ä¿ô¤Ï¡¢502¸Ä¡£

°ÊÁ°¤ÎË¿¸¦µæ¼¼¤ÎÃæ¤Ë¡¦¡¦¡¦(^^)

1/503=0.a¡¦¡¦¡¦b ¡Ên ·å¡Ë¤Î·«¤êÊÖ¤·¤È¤¹¤ë¤È¡¢1/503=a¡¦¡¦¡¦b/9¡¦¡¦¡¦9 (n ·å¡Ë¤Ç¤¤¤¤¤Î¤«¡ª
¤¿¤È¤¨¤Ð¡¢1/13=0.076923 ¤Î·«¤êÊÖ¤·¤Ê¤Î¤Ç¡¢1/13=76923/999999
13*76923=999999 ¤È6·å¤Î9¡¥
¥Õ¥§¥ë¥Þ¡¼¤Î¾®ÄêÍý¤«¤é¤Ï¡¢10^12-1 ¤¬¡¡13 ¤Ç³ä¤êÀÚ¤ì¤ë¤³¤È¤¬¸À¤¨¤ë¤«¤é¡¢12·å¤Î9¡£
°Ê¾å¤«¤é¡¢ºÇ¾®¤Î9¤Î·å¿ô¤¬Â¸ºß¤¹¤ë¤È¤­¤Ï¡¢p-1 ¤ÎÌó¿ô¤Î·å¤ÎÃæ¤Ë¤¢¤ë¤³¤È¤Ï¸À¤¨¤ë¡£

1/503 ¤Î½Û´Ä¾®¿ô¤Ï·×»»¤¬ÂçÊѤ½¤¦¤ÇÅÓÃæ¤Ç¤ä¤á¤Þ¤·¤¿¡£¡£¡£(^^;
¤À¤Ã¤Æ¡¢502=2*251 ¤Ê¤Î¤Ç¡¢¤¢¤ë¤È¤·¤Æ¤â¡¢251 ·å¤Î½Û´Ä¾®¿ô¤¸¤ã¤Ê¤¤¤Ç¤¹¤«¡ª¡ª
¶â¸÷¡¡¡¡ 5·î26Æü¡Ê¶â¡Ë 18:11:19¡¡¡¡ MAIL:kennji72001@yahoo.co.jp ¡¡¡¡27488
uchinyan
#27488
¤¦¡¢Í­Ì¾ÌäÂê¤Ç¤·¤¿¤«¡£¤¿¤À¡¢¤³¤ÎÀâÌÀ¤Ç¤Ï¡¢Â¾¤Î¿Í¤Ïʬ¤«¤é¤Ê¤¤¤«¤â¤·¤ì¤Ê¤¤¤Ê¡£

¥Ý¥¤¥ó¥È¤Ï¡¢»ä¤Î#27478¤Î
¡ä»ä¤Î¾ì¹ç¤Ï¡¢66..66 ¤«¤é¡¢2/3 = 0.666..., 1/3 = 0.333..., 3 * 1/3 = 1 = 0.999... ¤À¤Ê¤¡¡¢¤ÈÏ¢ÁÛ¤µ¤ì¡¢
¤ÎÊÕ¤ê¤Ç¤¹¡£1 = 3 * 1/3 = 3 * 0.333¡Ä = 0.999¡Ä ¤Ê¤Î¤Ç¡¢
1/503 = 0.999¡Ä ¡à 503 ¤È¤Ê¤Ã¤Æ¡¢1/503 ¤Î³ä¤ê»»¤ÎÃæ¤ËÅú¤¨¤¬¤¢¤ê¤Þ¤¹¡£
503 ¤ÏÁÇ¿ô¤Ê¤Î¤Ç¡¢1/503 ¤ÏÈó½Û´ÄÉôʬ¤Î¤Ê¤¤½Û´Ä¾®¿ô¤È¤Ê¤ê¤Þ¤¹¡£
½Û´Ä¾®¿ô¤Î½Û´ÄÉôʬ¤Î°ì¼þ´ü¤ÎŤµ¤Ï¡¢°ìÈ̤ˡ¢10^x ¢á 1 (mod p) ¤Î x ¤ÎÌó¿ô¤Ë¤Ê¤ê¤Þ¤¹¡£
¤³¤ì¤Ï¡¢¼ÂºÝ¤Ë³ä¤ê»»¤ò¤·¤Æ¤ß¤ì¤Ðʬ¤«¤ë¤È»×¤¤¤Þ¤¹¡£
p ¤òÁÇ¿ô¤È¤¹¤ë¤È¡¢¥Õ¥§¥ë¥Þ¡¼¤Î¾®ÄêÍý¤è¤ê¡¢É¬¤º¡¢10^(p-1) ¢á 1 (mod p) ¤¬¤¤¤¨¤ë¤Î¤Ç¡¢
¾¯¤Ê¤¯¤È¤â¡¢1/p ¤Î½Û´ÄÉôʬ¤Ï p-1 ¤ÎÌó¿ô¤Ë¤è¤ë¼þ´ü¡¢Ä¹¤µ¡¢¤ò¤â¤Á¤Þ¤¹¡£
¤·¤¿¤¬¤Ã¤Æ¡¢ÅöÁ³¡¢p-1 ¤Ç¤â¡¢·«¤êÊÖ¤·¤Þ¤¹¡£
Àè¤Û¤É¤Î 1/503 = 0.999¡Ä ¡à 503 ¤ËÌá¤ë¤È¡¢±¦Êդϡ¢999¡Ä99 ¤Î·Á¤ò³ä¤ë¤³¤È¤Ë¤Ê¤ê¤Þ¤¹¤¬¡¢
½Û´ÄÉôʬ¤´¤È¤Ë°ì¶èÀÚ¤ê¤Ë¤Ê¤ë¤Î¤Ç¡¢¤Á¤ç¤¦¤É¡¢½Û´ÄÉôʬ¤ÎŤµ¡¢µÚ¤Ó¤½¤ÎÇÜ¿ô¡¢¤Î 9 ¤Î¸Ä¿ô¤À¤±¤Î 999¡Ä99 ¤ò³ä¤êÀڤ뤳¤È¤Ë¤Ê¤ê¤Þ¤¹¡£
¿ô¼°Åª¤Ë¤Ï¡¢½Û´ÄÉôʬ¤ÎŤµ¤ò n ¤È¤·¤Æ¡¢
1/p = 0.abcd¡Äxyzabcde¡Äxyzabcd¡Äxyz¡Ä
10^n * 1/p = abcd¡Äxyz.abcde¡Äxyzabcd¡Äxyz¡Ä
(10^n - 1) * 1/p = abcd¡Äxyz
999¡Ä999 = p * abcd¡Äxyz, ¤¿¤À¤·¡¢999¡Ä999 ¤Ï 9 ¤¬ n ¸Äʤó¤Ç¤¤¤ë
¤È¤¤¤¦¤³¤È¤Ç¤¹¤Í¡£
º£¤Î¾ì¹ç¤Ï¡¢p = 503 ¤Ê¤Î¤Ç¡¢Åú¤¨¤Ï¡¢502 ¤Ç¤·¤¿¡££µ£°£²²ó¤Ë¤â°ú¤Ã³Ý¤±¤Æ¤ß¤Þ¤·¤¿ (^^;

¤Ê¤ª¡¢503 ¤Î¾ì¹ç¤Ë 502 ¤¬ºÇ¾®¤«¡¢°ìÈ̤ˡ¡p ¤Î¾ì¹ç¤Ë p-1 ¤¬ºÇ¾®¤«¡¢¤È¤¤¤¦¤Î¤Ï¡¢
503 ¤Î¾ì¹ç¤Ë¤Ï¡¢³Î¤«¤Ë 502 ¤¬ºÇ¾®¤Ë¤Ê¤Ã¤Æ¤¤¤ë¤Î¤Ç¤¹¤¬¡¢°ìÈ̤ˤϡ¢¤¢¤Þ¤ê´Êñ¤Ç¤Ï¤Ê¤¤¤Ç¤¹¡£
°ÊÁ°¤Ë¡¢Â¾¤Î¥µ¥¤¥È¤ÎÌäÂê¤ÎȯŸ¤Ç¸¡Æ¤¤·¤¿¤³¤È¤¬¤¢¤ê¤Þ¤¹¤¬¡¢¤³¤ì¤Ï¡¢10 ¤¬ p ¤Î¸¶»Ïº¬¡¢¤È¤¤¤¦¤Î¤Ë¤Ê¤Ã¤Æ¤¤¤Ê¤¤¤È¥À¥á¤À¤½¤¦¤Ç¡¢
¤½¤ÎȽÄê¤Ï¡¢¤¢¤Þ¤êÍưפǤϤʤ¤¤è¤¦¤Ç¤¹¡£¾¯¤Ê¤¯¤È¤â¡¢»ä¤Ë¤Ïʬ¤«¤ê¤Þ¤»¤ó¡£
Î㤨¤Ð¡¢7 ¤Ï 6 ¤¬ºÇ¾®¤Ç¤¹¤¬¡¢11 ¤Ï mod 11 ¤Ç 10 ¢á -1, 10^2 ¢á 1 ¤È¤Ê¤ê¡¢½Û´ÄÉôʬ¤ÎŤµ¤Ï 2 ¤Ë¤Ê¤ê¤Þ¤¹¡£
¤â¤·¤É¤Ê¤¿¤«¡¢¤³¤³¤é¤ÎȽÄê¤Ë¤Ä¤¤¤Æ¤´Â¸ÃΤǤ·¤¿¤é¡¢¤´¶µ¼¨´ê¤¤¤¿¤¯¡¥¡¥¡¥
¥Í¥³¤Î½»¤à²È¡¡¡¡ 5·î26Æü¡Ê¶â¡Ë 18:11:18¡¡¡¡ MAIL:uchi@sco.bekkoame.ne.jp ¡¡¡¡27489
uchinyan
#27488
¡ä1/503 ¤Î½Û´Ä¾®¿ô¤Ï·×»»¤¬ÂçÊѤ½¤¦¤ÇÅÓÃæ¤Ç¤ä¤á¤Þ¤·¤¿¡£¡£¡£(^^;
¤´»²¹Í¤Þ¤Ç¤Ë¡£
1/503 =
0.
0019880715705765407554671968190854870775347912524850894632206759443339960238568588469184890656063618
2902584493041749502982107355864811133200795228628230616302186878727634194831013916500994035785288270
3777335984095427435387673956262425447316103379721669980119284294234592445328031809145129224652087475
1491053677932405566600397614314115308151093439363817097415506958250497017892644135188866799204771371
7693836978131212723658051689860834990059642147117296222664015904572564612326043737574552683896620278
33
0019880715705765407554671968190854870775347912524850894632206759443339960238568588469184890656063618
2902584493041749502982107355864811133200795228628230616302186878727634194831013916500994035785288270
3777335984095427435387673956262425447316103379721669980119284294234592445328031809145129224652087475
1491053677932405566600397614314115308151093439363817097415506958250497017892644135188866799204771371
7693836978131212723658051689860834990059642147117296222664015904572564612326043737574552683896620278
33
¡Ä
³Î¤«¤Ë¡¢¼þ´ü 502 ¤Ç·«¤êÊÖ¤·¤Þ¤¹¡£
¥Í¥³¤Î½»¤à²È¡¡¡¡ 5·î26Æü¡Ê¶â¡Ë 18:19:39¡¡¡¡ MAIL:uchi@sco.bekkoame.ne.jp ¡¡¡¡27490
Ì´
°ãÈ¿¤Ê¤¬¤éÅùÈæµé¿ô¤Ç(4/9)¡ö¡Ê10¡°60+10¡°30-2)¤¬½Ð¤Þ¤¹¡£
¤Ç¡¢¡á(4/9)*(999¡¦¡¦¡¦99(60¸Ä)+999¡¦¡¦¡¦99(30¸Ä))
¡¡¡¡¡á444¡¦¡¦¡¦44(60¸Ä)+444¡¦¡¦¡¦44(30¸Ä)¤È¤Ê¤ê¤Þ¤¹¡£
¡¡¡¡ 5·î27Æü¡ÊÅÚ¡Ë 0:12:48¡¡¡¡ ¡¡¡¡27491
Ì´
¤¨¤¨¤È¡¢5/25¤Î18:43¤Ë̾Á°¤ò½ñ¤¤¤Æ¡Ö£³£¶£°¡×¤ÈÁ÷¤Ã¤Æ¤¢¤ë¤Ï¤º¤Ê¤Î¤Ë¥é¥ó¥­¥ó¥°¤Ë¤Ê¤¤¤ó¤Ç¤¹¤¬¡¢¡©¡©¡©¡Ê¼Â¤Ï¤á¤Ã¤¿¤Ë¥Ñ¥½¥³¥ó¤Ç¤­¤Ê¤¤¤ó¤Ç¤¹¤è¡£¡Ë
¡¡¡¡ 5·î27Æü¡ÊÅÚ¡Ë 0:22:46¡¡¡¡ MAIL:max_and_yume_forever@yahoo.co.jp ¡¡¡¡27492
¥¹¥â¡¼¥¯¥Þ¥ó
#27491
66¡¦¡¦¡¦6=6(10^29+10^28+¡¦¡¦¡¦+10+1)=6*1/9*(10^30-1)
66¡¦¡¦¡¦8=6*1/9*(10^30-1)+2
66¡¦¡¦¡¦6*66¡¦¡¦¡¦8=4/9*(10^60+10^30-2) ¤Ç¤«¡ª
²ÚÎï¤Ç¤¹¤Í¡Á

#27488
½Û´Ä¾®¿ô¤Î¾ì¹ç¡¢Í¾¤ê¤Ç¤¢¤ë¤È¤³¤í¤Î¼¡¤Ë³ä¤é¤ì¤ë¿ô¤Ï³ä¤ë¿ô°Ê²¼¤Ç¤·¤«¤â¤½¤Î¿ô¤Ï´Þ¤Þ¤Ê¤¤¤Î¤Ç¡¢
¤¿¤È¤¨¤Ð¡¢³ä¤ë¿ô¤¬ 503 ¤Ê¤é¡¢³ä¤é¤ì¤ë¿ô¤Ï¡¡1¡Á502 ¤·¤«½Ð¸½¤·¤Ê¤¤¤Ï¤º¤Ç¡¢¤Ä¤Þ¤ê¤Ï¡¢Â¿¤¯¤È¤â¡¢502 ²ó¤Þ¤Ç¤Ë¤Ï½Û´Ä¤¹¤ë¤Ï¤º¤È¤¤¤¦¤³¤È¤Ï¸À¤¨¤Þ¤¹¤Í¡£¡Ê;¤ê¤À¤«¤éÅöÁ³¤Ç¤¹¤Í¡ª¡Ë

¸¶»Ïº¬¤Ï¿ôÏÀ¤ÎËܤǤϴðÁääݤ¤¤è¤¦¤Ç¤¹¤¬¡¢¤ï¤¿¤·¤â¤¤¤Þ¤¤¤Á¥Ô¥ó¤ÈÍè¤Æ¤Þ¤»¤ó¡£¡£¡£(^^;

¶â¸÷¡¡¡¡ 5·î27Æü¡ÊÅÚ¡Ë 10:47:59¡¡¡¡ MAIL:kennji72001@yahoo.co.jp ¡¡¡¡27493
uchinyan
#27491, #27493
·ë¶É¤ÏƱ¤¸¤³¤È¤Ê¤Î¤Ç¤¹¤¬¡¢¾¯¤·ÏÃÂê¤Ë¤·¤¿½Û´Ä¾®¿ô¤ò»È¤¨¤Ð¡¢ÅùÈæ¿ôÎó¤ò»ý¤Á½Ð¤µ¤Ê¤¯¤Æ¤â¡¢»»¿ôŪ¤Ë¡¢Æ±¤¸¤³¤È¤¬¤Ç¤­¤Þ¤¹¡£
6/9 = 0.666¡Ä ¤Ê¤Î¤Ç¡¢
666¡Ä(30¸Ä)¡Ä666 = 666¡Ä(30¸Ä)¡Ä666.666¡Ä - 0.666¡Ä = 0.666¡Ä * 10^30 - 0.666¡Ä = 6/9 * 10^30 - 6/9 = 6/9 * (10^30 - 1)
¸å¤Ï¡¢Æ±¤¸¤Ç¤¹¡£

ºÙ¤«¤¤¥Æ¥¯¥Ë¥Ã¥¯Åª¤Ê¹©ÉפϤ¤¤í¤¤¤í¤¢¤ë¤è¤¦¤Ç¤¹¡£
#27467, #27468, #27477 °Ê³°¤Ë¤â¡¢»÷¤¿¤ê´ó¤Ã¤¿¤ê¤Ç¤¹¤¬¡¢
666¡Ä(30¸Ä)¡Ä666 * 666¡Ä(29¸Ä)¡Ä668
= 2 * 3 * 111¡Ä(30¸Ä)¡Ä111 * 4 * 166¡Ä(28¸Ä)¡Ä667
= 888¡Ä(30¸Ä)¡Ä888 * 500¡Ä(28¸Ä)¡Ä001
= 444¡Ä(30¸Ä)¡Ä444888¡Ä(30¸Ä)¡Ä888
¤Ê¤ó¤Æ¤Î¤â¤¢¤ê¤Þ¤¹¤Í¡£
¡Ö¤À¤«¤é¤É¤¦¤·¤¿¡©¡×¤È¤¤¤¦´¶¤¸¤â¤¢¤ê¤Þ¤¹¤¬¡¥¡¥¡¥(^^;
¥Í¥³¤Î½»¤à²È¡¡¡¡ 5·î27Æü¡ÊÅÚ¡Ë 11:38:10¡¡¡¡ MAIL:uchi@sco.bekkoame.ne.jp ¡¡¡¡27494
¥¹¥¤¥«
½é¤á¤ÆÄ©À路¤¿¤Î¤Ç¤¹¤¬¤ß¤Ê¤µ¤ó¤Ï¤É¤ì¤°¤é¤¤¤Î´ü´ÖÄ©Àï¤Ê¤µ¤Ã¤Æ¤¤¤ë¤Î¤Ç¤¹¤«¡£
¡¡
¤Þ¤¿¼ºÎé¤Ç¤¹¤¬£±£±ºÐ¤ÎÊý¤Ï¡¢¤¤¤Þ¤¹¤«¡©µ¤¤Ë¤Ê¤Ã¤Æ¤·¤Þ¤Ã¤Æ¡¦¡¦¡¦¡£
¤Á¤Ê¤ß¤Ë¤Ü¤¯¤Ï¡¢£±£±ºÐ¤Ç¤¹¡£
¡¡¡¡ 5·î27Æü¡ÊÅÚ¡Ë 21:53:59¡¡¡¡ ¡¡¡¡27495
¥¹¥â¡¼¥¯¥Þ¥ó
#27495
¥¹¥¤¥«¤µ¤ó¤Ø¡£
¤ï¤¿¤·¤Ï¿ôǯÁ°¤«¤é¥¢¥¯¥»¥¹¡Ê¸¡º÷¤·¤Æ¸«¤Ä¤±¤Þ¤·¤¿¡£¡Ë¤¹¤ë¤è¤¦¤Ë¤Ê¤ê¤Þ¤·¤¿¡£º£¤Ç¤Ï¤³¤³¤Ë¤Ï¤Þ¤Ã¤Æ¤Þ¤¹¡£(^^)
11ºÐ¤È¤¤¤¨¤Ð¤Þ¤À¾®5¤Ç¤¹¤è¤Í¡©¤¦¤Á¤Î°ìÈÖ²¼¤Î»Ò¡ÊÃæ3¡Ë¤âPC¤¤¤¸¤Ã¤Æ¤ë¤±¤É¡¢Í§Ã£¤È¤Î¥á¡¼¥ë¤Ð¤Ã¤«¤ê¤·¤Æ¤Þ¤¹¤è¡£º£¤Ï¥¤¥ó¥¿¡¼¥Í¥Ã¥È¤È¤¤¤¦²¿¤Ç¤â¤Ç¤­¤ë´Ä¶­¤¬¤¢¤Ã¤Æ¤¦¤é¤ä¤Þ¤·¤¤¤Í¡ª
¶â¸÷¡¡¡¡ 5·î28Æü¡ÊÆü¡Ë 8:14:27¡¡¡¡ MAIL:kennji72001@yahoo.co.jp ¡¡¡¡27496
¥¹¥â¡¼¥¯¥Þ¥ó
µ×¤·¤Ö¤ê¤Îͧ¿ÍÌä

½é¹à¤Ë3¤ò¼¡¡¹¤È¤«¤±¤Æ¼¡¤Î¹à¤¬½ÐÍè¤ë¿ôÎó
1,3,9,27,81,243,729,¡¦¡¦¡¦
¤¬¤¢¤ë¡£¤³¤Î¿ôÎ󤫤餳¤È¤Ê¤ë¤¤¤¯¤Ä¤«¤Î¿ô¤ò¤È¤Ã¤Æ­¤·¤Æ
¤Ç¤­¤ë¿ô¤ò¾®¤µ¤¤½ç¤Ëʤ٤ƽÐÍè¤ë¿ôÎó
1,3,4,9,10,12,13,¡¦¡¦¡¦
¤ò¹Í¤¨¤ë¤È¤­¡¢¤³¤Î¿ôÎó¤Î100ÈÖÌܤοô¤Ï²¿¤«¡£
¶â¸÷¡¡¡¡ 5·î28Æü¡ÊÆü¡Ë 13:34:01¡¡¡¡ MAIL:kennji72001@yahoo.co.jp ¡¡¡¡27497
uchinyan
#27497
·×»»°ã¤¤¤¬¤Ê¤±¤ì¤Ð¡¥¡¥¡¥
981
Æó¿ÊË¡¡Ü»°¿ÊË¡
ͭ̾Ìä¤Ç¤Ï¡©¡¡´ª°ã¤¤¤«¤Ê¡¥¡¥¡¥
¥Í¥³¤Î½»¤à²È¡¡¡¡ 5·î28Æü¡ÊÆü¡Ë 14:07:35¡¡¡¡ MAIL:uchi@sco.bekkoame.ne.jp ¡¡¡¡27498
£ø£ð
666¡ß668¡á444888¡¡6666¡ß6668¡á44448888¡¡
666¡Ä66¡ß666¡Ä68¡á4444¡Ä48888¡Ä8¤Ç½ÐÍè¤ë¤Ï¤º¤Ç¤¹

¡¡¡¡ 5·î28Æü¡ÊÆü¡Ë 14:17:44¡¡¡¡ ¡¡¡¡27499
¥¹¥â¡¼¥¯¥Þ¥ó
#27498
uchinyan¤µ¤ó¡¢Àµ²ò¡ª

¤³¤ì¤Ã¤Æͭ̾Ìä¤Ê¤ó¤Ç¤¹¤«¡£¡£¡£¤­¤ì¤¤¤ÊÌäÂê¤Ç¤¹¤â¤Î¤Í¡£
¤Á¤Ê¤ß¤Ë²òÅú¤ò¤Ð¡£
Í¿¤¨¤é¤ì¤¿¿ôÎó¤ò3¿ÊË¡¤Çɽ¤¹¤È
1¡¢10¡¢100¡¢1000¡¢¡¦¡¦¡¦
ÌäÂê¤ÎÁàºî¤Ë¤è¤Ã¤Æ½ÐÍè¤ë¿ôÎó¤Ï3¿ÊË¡¤Ç
1¡¢10¡¢11¡¢100¡¢101¡¢110¡¢111¡¢1000¡¢1001¡¢¡¦¡¦¡¦
¤³¤ì¤Ï2¿ÊË¡¤È¤ß¤Ê¤¹¤È¼«Á³¿ô¤¬1¤«¤é¤â¤ì¤Ê¤¯
½çÈ֤ˤʤé¤ó¤Ç¤¤¤ë¡£
2¿Ê¿ô¤Ç100=1100100
¤è¤Ã¤Æµá¤á¤ë¿ô¤Ï3^6+3^5+3^2=981

¶â¸÷¡¡¡¡ 5·î28Æü¡ÊÆü¡Ë 14:22:24¡¡¡¡ MAIL:kennji72001@yahoo.co.jp ¡¡¡¡27500
uchinyan
#27500
¾¯¤Ê¤¯¤È¤â¡¢£²¡¢£³¤Î¥µ¥¤¥È¤Ç¸«¤¿Ëô¤Ï²ò¤¤¤¿¤è¤¦¤Êµ¤¤¬¤·¤Æ¤Þ¤¹¤¬¡¥¡¥¡¥
¤Ç¤â¡¢ÃΤé¤Ê¤¤Êý¤â¤¤¤Þ¤¹¤è¤Í¤§¡¢¤­¤Ã¤È¡£
º£ÅÙ¤«¤é¡¢¤½¤¦¤¤¤¦»þ¤Ï¡¢ÌۤäƤª¤­¤Þ¤¹ (^^;
¥Í¥³¤Î½»¤à²È¡¡¡¡ 5·î28Æü¡ÊÆü¡Ë 15:00:04¡¡¡¡ MAIL:uchi@sco.bekkoame.ne.jp ¡¡¡¡27501
uchinyan
¤È¤¢¤ë·Ç¼¨ÈĤǸ«¤¿ÌäÂê¤Ç¤¹¤¬¡¢¤³¤ó¤ÊÌäÂê¤Ï¤É¤¦¤Ç¤·¤ç¤¦¤«¡©
¤ª²Ë¤Ê¤é¤Ð¡¥¡¥¡¥

°ì¤Î°Ì¤¬£´¤Ç¡¢¤½¤Î£´¤òÀèƬ¤Ë¤â¤Ã¤Æ¤¯¤ë¤È¡¢¸µ¤Î£²ÇܤȤʤëºÇ¾®¤Î¼«Á³¿ô¤Î·å¿ô¤òµá¤á¤Æ¤¯¤À¤µ¤¤¡£
¤¢¡¢É½µ­Ë¡¤Ï10¿ÊË¡¤Ç¤¹¡£
;͵¤¬¤¢¤ì¤Ð¡¢ºÇ¾®¤Î¼«Á³¿ô¼«ÂΡ¢ºÇ¾®¤Ç¤Ï¤Ê¤¤¾ì¹ç¤Ï¤É¤¦¤Ê¤ë¤Î¤«¡¢¤â¹Í¤¨¤Æ¤ß¤Æ¤¯¤À¤µ¤¤¡£

¤Ê¤ª¡¢º£¤Þ¤Ç¤Î·Ç¼¨ÈĤÎÏÃÂê¤È¾¯¤·´Ø·¸¤¬¤¢¤ê¤Þ¤¹¡£
¥Í¥³¤Î½»¤à²È¡¡¡¡ 5·î29Æü¡Ê·î¡Ë 14:09:00¡¡¡¡ MAIL:uchi@sco.bekkoame.ne.jp ¡¡¡¡27502
¥¹¥â¡¼¥¯¥Þ¥ó
#27502
>°ì¤Î°Ì¤¬£´¤Ç¡¢¤½¤Î£´¤òÀèƬ¤Ë¤â¤Ã¤Æ¤¯¤ë¤È¡¢¸µ¤Î£²ÇܤȤʤëºÇ¾®¤Î¼«Á³¿ô¤Î·å¿ô¤òµá¤á¤Æ¤¯¤À¤µ¤¤¡£
¤¢¡¢É½µ­Ë¡¤Ï10¿ÊË¡¤Ç¤¹¡£
;͵¤¬¤¢¤ì¤Ð¡¢ºÇ¾®¤Î¼«Á³¿ô¼«ÂΡ¢ºÇ¾®¤Ç¤Ï¤Ê¤¤¾ì¹ç¤Ï¤É¤¦¤Ê¤ë¤Î¤«¡¢¤â¹Í¤¨¤Æ¤ß¤Æ¤¯¤À¤µ¤¤¡£

Ãà°ì·×»»¤·¤Æ¡¢
210526315789473684 ¤Î18·å¡£
ºÇ¾®¤Ç¤Ê¤¤¾ì¹ç¤Ï¡¢¤³¤Î·«¤êÊÖ¤·¤À¤«¤é¡¢18¤ÎÇÜ¿ô·å¡£

¤â¤È¤Î¿ô¤òn·å¤È¤¹¤ë¡£¤â¤È¤Î¿ô¤ò10*x+4 ¤È¤¹¤ë¤È¡¢x¤Ï n-1 ·å¡£
4*10^(n-1)+x=2(10*x+4) ¤À¤«¤é¡¢
19x=4*10^(n-1)-8
10^18-1=(10^9-1)(10^9+1)¢á0 (mode 19)
¤Ä¤Þ¤ê¡¢19x ¤Ï¡¢18·å¤«¡¢9·å¤«¡¢3·å¤¬¸À¤¨¤ë¡£
1/19=x/99¡¦¡¦¡¦9 ¤Ê¤Î¤Ç¡¢·×»»¤¹¤ë¤È¡¢
1/19=0.052631578947368421 ¤Î½Û´Ä¾¯¿ô¡£
x ¤Ï¡¢17 ·å¤Ê¤Î¤Ç¡¢¤â¤È¤Î¿ô¤Î·å¿ô¤Ï18 ¤¬ºÇ¾®·å¿ô¤Èʬ¤«¤ë¡£

¤·¤«¤·¡¢x ¤ÈºÇ½éµá¤á¤¿¿ô 21052631578947368(4) ¤È°ã¤¦¤Ê¤¢¡¦¡¦¡¦¡©
¶â¸÷¡÷²¬»³¡¡¡¡ 5·î29Æü¡Ê·î¡Ë 17:58:54¡¡¡¡ MAIL:kennji72001@yahoo.co.jp ¡¡¡¡27503
uchinyan
#27503
¥¹¥â¡¼¥¯¥Þ¥ó¤µ¤ó¡¢²òÅú¤¢¤ê¤¬¤È¤¦¤´¤¶¤¤¤Þ¤¹¡£Àµ²ò¤Ç¤¹ ^^/
¾¯¤·¡¢¥³¥á¥ó¥È¤Ê¤É¡£

¡äÃà°ì·×»»¤·¤Æ¡¢
¡ä210526315789473684 ¤Î18·å¡£
¤³¤Î·×»»¤ò¾¯¤·¾Ü¤·¤¯½ñ¤¤¤Æ¤ª¤¯¤È¡¥¡¥¡¥
µá¤á¤ë¿ô¤Ï¡¢¡û4¡¢¤È½ñ¤±¤Þ¤¹¡£
4 ¤òÀèƬ¤Ë¤â¤Ã¤Æ¤¤¤¯¤È¡¢4¡û ¤Ç¡¢¤³¤ì¤¬ 2 * ¡û4 = ¢¢8 ¤ËÅù¤·¤¤¤Î¤Ç¡¢4¡û = ¢¢8 ¤È¤Ê¤ê¡¢
¡û ¼«ÂΤ¬ 2¡û8 ¤È½ñ¤±¤ë¤³¤È¤¬Ê¬¤«¤ê¤Þ¤¹¡£¤Ä¤Þ¤ê¡¢µá¤á¤ë¿ô¤Ï 2¡û84 ¤Ç¤¹¡£Æ±Íͤˤ·¤Æ¡¢
2¡û84 -> 42¡û8 = 4¢¢68 -> 2¡û684 -> 42¡û68 = 4¢¢368 -> 2¡û3684 -> 42¡û368 = 4¢¢7368 ->
2¡û73684 -> 42¡û7368 = 4¢¢47368 -> 2¡û473684 -> 42¡û47368 = 4¢¢947368 -> 2¡û9473684 -> 42¡û947368 = 4¢¢8947368 ->
2¡û89473684 -> 42¡û8947368 = 4¢¢78947368 -> 2¡û789473684 -> 42¡û78947368 = 4¢¢578947368 ->
2¡û5789473684 -> 42¡û578947368 = 4¢¢1578947368 -> 2¡û15789473684 -> 42¡û1578947368 = 4¢¢31578947368 ->
2¡û315789473684 -> 42¡û31578947368 = 4¢¢631578947368 -> 2¡û6315789473684 -> 42¡û631578947368 = 4¢¢2631578947368 ->
2¡û26315789473684 -> 42¡û2631578947368 = 4¢¢52631578947368 ->
2¡û526315789473684 -> 42¡û52631578947368 = 4¢¢052631578947368 ->
2¡û0526315789473684 -> 42¡û052631578947368 = 4¢¢1052631578947368 ->
2¡û10526315789473684 -> 42¡û1052631578947368 = 4¢¢21052631578947368 -> ¡û¡¢¢¢¤È¤â¤Ë¤Ê¤·¤Ç OK
¤Ç¡¢·ë¶É¡¢210526315789473684 ¤¬µá¤á¤ëºÇ¾®¤Î¿ô¤Ç¡¢·å¤Ï18·å¤Ë¤Ê¤ê¤Þ¤¹¡£

¤µ¤Æ¡¢¤½¤Î¸å¤ÎµÄÏÀ¤Ï¡¢Çطʤòõ¤ë°ÕÌ£¤Ç½ÅÍפǤ¹¡£
¡ä¤â¤È¤Î¿ô¤òn·å¤È¤¹¤ë¡£¤â¤È¤Î¿ô¤ò10*x+4 ¤È¤¹¤ë¤È¡¢x¤Ï n-1 ·å¡£
¡ä4*10^(n-1)+x=2(10*x+4) ¤À¤«¤é¡¢
·ë¶É¡¢x = (4 * 10^(n-1) - 8)/19 ¤Ç¤¹¤Í¡£
¡ä¤·¤«¤·¡¢x ¤ÈºÇ½éµá¤á¤¿¿ô 21052631578947368(4) ¤È°ã¤¦¤Ê¤¢¡¦¡¦¡¦¡©
µá¤á¤ë¤Î¤Ï¡¢x ¤Ç¤Ï¤Ê¤¯¡¢10 * x + 4 ¤Ç¡¢¤·¤«¤â¡¢x = (4 * 10^(n-1) - 8)/19 ¤Ê¤Î¤Ç¡¢
ÅöÁ³¤Î¤³¤È¤Ê¤¬¤é¡¢1/19 ¤Î½Û´ÄÉôʬ¤È¤Ï°Û¤Ê¤Ã¤Æ¤¤¤Þ¤¹¡£¤³¤ì¤Ë¤Ä¤¤¤Æ¤Ï¡¢¸å¤Ç²òÀ⤷¤Þ¤¹¡£
¤½¤ì°Ê³°¤Ï½ñ¤«¤ì¤Æ¤¤¤ëÄ̤ê¤Ç¤¹¤¬¡¢x ¤¬À°¿ô¤Ê¤Î¤Ç¡¢
4 * 10^(n-1) - 8 ¢á0 (mod 19)
10^(n-1) ¢á 2 (mod 19)
µÄÏÀ¤µ¤ì¤Æ¤¤¤ëÄ̤ꡢ10^k ¢á 1 (mod 19) ¤ÎºÇ¾®¤Î k ¤Ï 18 ¤Ê¤Î¤Ç¡¢
10^18 ¢á 1 ¢á 20 (mod 19)
10^17 ¢á 2 (mod 19)
¤È¤Ê¤ê¡¢ºÇ¾®¤Î n ¤Ï¡¢n - 1 = 17 ¤è¤ê n = 18 ¤Ç¡¢µá¤á¤ëºÇ¾®¤Î¿ô¤Î·å¿ô¤¬ 18 ·å¤Ê¤Î¤Ï¡¢
1/19 ¤Î¾®¿ôÂè10°Ì¤°¤é¤¤¤Þ¤Ç¤Î·×»»¤Çʬ¤«¤ê¤Þ¤¹¡£
¤â¤Ã¤È¤â¡¢ºÇ¾®¤Î¿ô¼«ÂΤϡ¢´èÄ¥¤Ã¤Æ¡¢½Û´Ä¤¹¤ë¤Þ¤Ç¤ä¤é¤Ê¤¤¤È¥À¥á¤Ç¤¹¤¬¡£
¤Ê¤ª¡¢°ìÈ̲ò¤Ï¡¢10^18 ¢á 1 (mod 19) ¤ËÃí°Õ¤·¤Æ¡¢
10 * (4 * 10^(n-1) - 8)/19 + 4, ¤¿¤À¤· n ¤Ï n ¢á 0 (mod 18) ¤È¤Ê¤ëÀµ¤ÎÀ°¿ô
¤È¤â½ñ¤±¤Þ¤¹¡£

¤³¤³¤Þ¤Ç¤¯¤ì¤Ð¡¢¤³¤ÎÌäÂê¤â½Û´Ä¾®¿ô¤È¿¼¤¤´Ø·¸¤¬¤¢¤ë¤³¤È¤¬Ê¬¤«¤ë¤È»×¤¤¤Þ¤¹¡£º£²ó¤Ï¡¢
1/19 = 0.052631578947368421052631578947368421¡Ä
¤Ç¤¹¡£¼¡¤Î´Ø·¸¡¢
2/19 = 20/10 * 1/19 = (1/10 + 19/10) * 1/19 = 1/10 * 1/19 + 1/10
4/19 = 2 * 2/19 = 1/10 * 2/19 + 2/10
¤ò»È¤¦¤È¡¢
1/19 = 000.052631578947368421052631578947368421¡Ä
2/19 = 00.1052631578947368421052631578947368421¡Ä
4/19 = 0.21052631578947368421052631578947368421¡Ä
¤Ê¤Î¤Ç¡¢
10 * (4 * 10^(n-1) - 8)/19 + 4 = 10^n * 4/19 - 80/19 + 4 = 10^n * 4/19 - 4/19
¤«¤é¡¢µá¤á¤ë¿ô¤Ï¡¢4/19 ¤Î¾®¿ôÉôʬ¤¬ÂǤÁ¾Ã¤¹¤è¤¦¤Ë¤¹¤ì¤Ð¤¤¤¤¤Î¤Ç¡¢
10^18 * 4/19 = 210526315789473684.21052631578947368421052631578947368421¡Ä
00000 + 4/19 = 000000000000000000.21052631578947368421052631578947368421¡Ä
¤³¤³¤Ç¡¢¡Ö00000 + ¡×¤Ï¡¢Ê¸»ú·¤¨¤Î¤¿¤á¤Ç°ÕÌ£¤Ï¤¢¤ê¤Þ¤»¤ó¡£
¤½¤³¤Ç¡¢µá¤á¤ëºÇ¾®¤Î¿ô¤Ï¡¢210526315789473684 ¤Ç¡¢·å¿ô¤Ï 18 ·å¡¢¤È¤¹¤ë¤³¤È¤â¤Ç¤­¤Þ¤¹¡£

º£²ó¤ÎÌäÂê¤Ë¤«¤³¤Ä¤±¤ÆÍ·¤ó¤Ç¤ß¤Þ¤·¤¿¤¬¡¢½Û´Ä¾®¿ô¤Ï¤¤¤í¤¤¤í¤ÈÌÌÇò¤¤¤Ç¤¹¤Í ^^/
¥Í¥³¤Î½»¤à²È¡¡¡¡ 5·î30Æü¡Ê²Ð¡Ë 12:43:25¡¡¡¡ MAIL:uchi@sco.bekkoame.ne.jp ¡¡¡¡27504
¥¹¥â¡¼¥¯¥Þ¥ó
#27504
1/19 = 0.052631578947368421 052631578947368421¡¦¡¦¡¦
2/19 = 0.105263157894736842 105263157894736842¡¦¡¦¡¦
3/19 = 0.157894736842105263 157894736842105263¡¦¡¦¡¦
4/19 = 0.210526315789473684 210526315789473684¡¦¡¦¡¦

¤È¡¢ºÇ½é¤Î½Û´Ä¾®¿ô¤ò¤º¤é¤·¤¿¤â¤Î¤Ë¤Ê¤Ã¤Æ¤Þ¤¹¤Í¡©
¤Ê¤¼¤½¤¦¤Ê¤ë¤Î¤«¹Í¤¨¤Æ¤Þ¤·¤¿¤¬¡¢¡¢¡¢
³ä¤ê»»¤ò¤·¤Æ¤ë¤Î¤Ç¡¢ÁÇ¿ô¤Î19¤Î¾ì¹ç¡¢³ä¤é¤ì¤ë¿ô¤¬1¡Á18¤Þ¤Çɬ¤º½Ð¤Æ¤¯¤ë¤Î¤Ç¡Ê½Û´Ä¾®¿ô¤Î·å¤¬18·å¤«¤é¡Ë¡¢n/19 (1¡Án¡Á18) ¤Ï¡¢¤â¤È¤Î½Û´Ä¾®¿ô¤ÎÅÓÃ椫¤é¤Î·×»»¤ò¤¹¤ë¤³¤È¤ÈƱ¤¸¤ï¤±¤À¤«¤é¤½¤¦¤Ê¤ë¤ï¤±¤Ç¤¹¤Í¡ª
¤È¤Ê¤ë¤È¡¢²¼¤Î·å¤¬4°Ê³°¤Ç¤â¤½¤ì¤òÀèƬ¤Ë¤·¤¿¤È¤­¡¢¤â¤È¤ÎÇܤˤʤë¿ô¤Ï¡¢¸«Åö¤¬¤Ä¤­¤Þ¤¹¤Í¡ª
¤Á¤Ê¤ß¤Ë4¤Î¾ì¹ç¤Ï¡¢
736842105263157894¡¡¤«¡¢
210526315789473684¡¡¤Î¤¦¤Á¤Î¤¤¤º¤ì¤«¤À¤Èʬ¤«¤ê¡¢
ÌÀ¤é¤«¤ËÁ°¼Ô¤ÏËþ¤¿¤µ¤Ê¤¤¤«¤é¸å¼Ô¤Ç¤¢¤ë¤È¤ï¤«¤ê¤Þ¤¹¡£
Á°¼Ô¤Ï¡¢²¼¤Î4¤òÀèƬ¤Ë»ý¤Ã¤Æ¤­¤¿¤È¤­¤â¤È¤Î9Çܤοô¤Ë¤Ê¤ê¤Þ¤¹¤Í¡£
¶â¸÷¡÷²¬»³¡¡¡¡ 5·î30Æü¡Ê²Ð¡Ë 13:50:23¡¡¡¡ MAIL:kennji72001@yahoo.co.jp ¡¡¡¡27505
uchinyan
#27505
¡ä³ä¤ê»»¤ò¤·¤Æ¤ë¤Î¤Ç¡¢ÁÇ¿ô¤Î19¤Î¾ì¹ç¡¢³ä¤é¤ì¤ë¿ô¤¬1¡Á18¤Þ¤Çɬ¤º½Ð¤Æ¤¯¤ë¤Î¤Ç¡Ê½Û´Ä¾®¿ô¤Î·å¤¬18·å¤«¤é¡Ë¡¢
¡än/19 (1¡Án¡Á18) ¤Ï¡¢¤â¤È¤Î½Û´Ä¾®¿ô¤ÎÅÓÃ椫¤é¤Î·×»»¤ò¤¹¤ë¤³¤È¤ÈƱ¤¸¤ï¤±¤À¤«¤é¤½¤¦¤Ê¤ë¤ï¤±¤Ç¤¹¤Í¡ª
¤Ï¤¤¡¢¤½¤¦¤¤¤¦¤³¤È¤Ç¤¹¡£
¤¿¤À¡¥¡¥¡¥
¡ä736842105263157894¡¡¤«¡¢
¡ä210526315789473684¡¡¤Î¤¦¤Á¤Î¤¤¤º¤ì¤«¤À¤Èʬ¤«¤ê¡¢
¡äÌÀ¤é¤«¤ËÁ°¼Ô¤ÏËþ¤¿¤µ¤Ê¤¤¤«¤é¸å¼Ô¤Ç¤¢¤ë¤È¤ï¤«¤ê¤Þ¤¹¡£
736842105263157894 ----> 473684210526315789
736842105263157894 * 2 = 1473684210526315788
·å¾å¤¬¤ê¤ÎÏä¬Íí¤ó¤Ç¤¯¤ë¤Î¤Ç¡¢¤´»ØŦ¤ÎÄ̤ꡢ»ÄÇ°¤Ê¤¬¤é¡¢Á°¼Ô¤Ï¥À¥á¤Ç¤¹¤Í¡£
¡äÁ°¼Ô¤Ï¡¢²¼¤Î4¤òÀèƬ¤Ë»ý¤Ã¤Æ¤­¤¿¤È¤­¤â¤È¤Î9Çܤοô¤Ë¤Ê¤ê¤Þ¤¹¤Í¡£
736842105263157894 ----> 473684210526315789
736842105263157894 * 9 = 6631578947368421046
Á´¤¯¤Ê¤é¤Ê¤¤¤Î¤Ç¤¹¤¬¡¥¡¥¡¥¤è¤¯Ê¬¤«¤é¤Ê¤¤¡¥¡¥¡¥
¥Í¥³¤Î½»¤à²È¡¡¡¡ 5·î30Æü¡Ê²Ð¡Ë 16:58:22¡¡¡¡ MAIL:uchi@sco.bekkoame.ne.jp ¡¡¡¡27507
¥¹¥â¡¼¥¯¥Þ¥ó
#27507
>¡äÁ°¼Ô¤Ï¡¢²¼¤Î4¤òÀèƬ¤Ë»ý¤Ã¤Æ¤­¤¿¤È¤­¤â¤È¤Î9Çܤοô¤Ë¤Ê¤ê¤Þ¤¹¤Í¡£
736842105263157894 ----> 473684210526315789
736842105263157894 * 9 = 6631578947368421046
Á´¤¯¤Ê¤é¤Ê¤¤¤Î¤Ç¤¹¤¬¡¥¡¥¡¥¤è¤¯Ê¬¤«¤é¤Ê¤¤¡¥¡¥¡¥

¼ºÎ餷¤Þ¤·¤¿¡£
Á´Á³´Ö°ã¤Ã¤Æ¤Þ¤¹¤Í¡£(^^;

°Ê²¼¤É¤¦¤Ç¤â¤¤¤¤¤³¤È¤Ç¤¹¤¬¡¢¡¢¡¢
³ä¤Ã¤¿Í¾¤ê¤¬¡¢1,10,5,12,6,3,11,15,17,18,9,14,7,13,16,8,4,2,¡¦¡¦¡¦
1¤«¤é9ÈÖÌܤÏ18¡§1+18=19
10¤«¤é9ÈÖÌܤÏ9¡§10+9=19
¡¦
¡¦
¡¦

1/19¤È11/19¡¡¤Ï²¼°ì·å¤¬1¤ÇƱ¤¸¤À¤«¤é¤º¤é¤·¤¿¤â¤Î¤Ë¤Ê¤ë¡£
2/19¤È12/19
¡¦
¡¦
¡¦
8/19 ¤È 18/19
9/19 ¤È¡¡¡©
10/19 ¤È¡¡¡©

9*2n ¤Î¤±¤¿¤¬Ê¤ֽ۴ľ®¿ô¤Ï¤ß¤ÊÁÇ¿ô¤Ç¤Ï¤Ê¤¤¤Ç¤¹¤Í¡£
¤Þ¤¿¡¢¤½¤ì¤À¤±¤Î¿ô¤ò¤Ç¤¿¤é¤á¤Ëʤ٤¿¤È¤­¡¢É¬¤º1¸Ä¤Ï1/n ¤Ë¤Ç¤­¤ë¤Ã¤Æ¤³¤È¤Ç¤¹¤Í¤¨¡£
18,36,54,72,90,108,126,144,162,180,198,216,234,¡¦¡¦¡¦
19,37,(55),73,(91),109,127,(145),163,181,199,217,(235),¡¦¡¦¡¦
¶â¸÷¡÷²¬»³¡¡¡¡ 5·î30Æü¡Ê²Ð¡Ë 22:45:29¡¡¡¡ MAIL:kennji72001@yahoo.co.jp ¡¡¡¡27508
¤à¤é¤«¤ß
Âçºå¥ª¥Õ³«ºÅ¤Ç¤¹¤«¡©
¡¡¡¡ 5·î31Æü¡Ê¿å¡Ë 13:54:04¡¡¡¡ MAIL:ryoiti@sansu.org ¡¡¡¡27509
µÈÀî¡¡¥Þ¥µ¥ë
#27509
¡¡¥Ï¥¤¡¢7/9¡ÊÆü¡Ë¤òͽÄꤷ¤Æ¤¤¤Þ¤¹¡££±¥ö·îÁ°¤Ë¤Ê¤Ã¤¿¤é¥¢¥Ê¥¦¥ó¥¹¤·¤è¤¦¡¢¤È¤«»×¤Ã¤Æ¤¤¤¿¤Î¤Ç¤¹¤¬¡¢¤É¤¦¤ä¤Ã¤ÆÃΤê¤Þ¤·¤¿¡©(^^;
PowerBook G4¡¡¡¡ 5·î31Æü¡Ê¿å¡Ë 18:51:04¡¡¡¡ MAIL:masaru-y@san¡¡su.org HomePage:»»¥Á¥ã¥ì¡¡¡¡27510