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3Â¥: Originally posted by feixiaolin at 2013-08-08 14:29:39
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ƽ·²Ò»ÈË: ½ð±Ò+3 2013-08-09 18:45:07
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http://en.wikipedia.org/wiki/Chinese_remainder_theorem
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3Â¥2013-08-08 14:29:39
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4Â¥: Originally posted by ƽ·²Ò»ÈË at 2013-08-09 18:56:43
Ò»¸öÈýλÊý³ýÒÔ9Óà7£¬³ýÒÔ5Óà2£¬³ýÒÔ4Óà3£¬ÇóÕâ¸öÈýλÊý£¿...

x=7 mod 9, 2 mod 5, 3 mod 4.
ÏÈÕÒÒ»¸öÊý, ËüÊÇ5ºÍ4µÄ±¶Êý, µ«Ä£9Óà1.   20*5=1 mod 9. ¼ÇÏÂ100.
ÔÙÕÒÒ»¸öÊý, ËüÊÇ9ºÍ4µÄ±¶Êý, µ«Ä£5Óà1.   36*1= 1 mod 5. ¼ÇÏÂ36.
ÀàËÆµØ, ÏÂÒ»¸öÄ¿±êÊÇ 45*1= 1 mod 4.
ËùÒÔ x= 7*100 + 2* 36 + 3* 45 =907.  Õ⹫ʽ¾ÍÊÇÖйúÊ£ÓඨÀí.

µ±È», ÕâÖ»ÊÇÒ»¸ö½â, Èç¹ûÄãҪͨ½â, ÒòΪ9,4,5×îС¹«±¶ÊýÊÇ180, ËùÒÔËùÓеĽâÐÎʽΪ 907+ n*180.
ÈýλÊýÀïÃæÓÐ187, 367, 547, 727, 907¹²5¸ö. Æäʵ, 7ÊÇ×îСÕýÕûÊýÂú×ãÌõ¼þµÄ.
5Â¥2013-08-10 00:19:39
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