BlogJava-helloworld 路慢慢其修远兮，吾上下而求索-随笔分类-数学定理http://www.blogjava.net/zhaochengming/category/28439.htmlzh-cnFri, 28 Dec 2007 07:12:28 GMTFri, 28 Dec 2007 07:12:28 GMT60最大公约数(Euclid算法)http://www.blogjava.net/zhaochengming/archive/2007/12/28/171148.htmlhelloworld2008helloworld2008Fri, 28 Dec 2007 04:48:00 GMThttp://www.blogjava.net/zhaochengming/archive/2007/12/28/171148.htmlhttp://www.blogjava.net/zhaochengming/comments/171148.htmlhttp://www.blogjava.net/zhaochengming/archive/2007/12/28/171148.html#Feedback0http://www.blogjava.net/zhaochengming/comments/commentRss/171148.htmlhttp://www.blogjava.net/zhaochengming/services/trackbacks/171148.htmlgcd(a,b) = gcd(b, a mod b)

求a,b的最大公约数d
有 a = bk + r
      a = x*d
      b = y*d
      ->
      r = a - bk (即a mod b)
      r = xd - ydk
      r = (x-yk)d
      即d也可以被a mod b整除,d是a mod b的公约数
      因为d是b的公约数
所以 gcd(b,a mod b)成立



helloworld2008 2007-12-28 12:48 发表评论
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