C++博客-richard-desktop-文章分类-数学http://www.cppblog.com/rchard/category/12798.htmlzh-cnSun, 10 Jan 2010 09:04:12 GMTSun, 10 Jan 2010 09:04:12 GMT60求正整数集合使得元素之和等于元素之积http://www.cppblog.com/rchard/articles/105339.htmlWentai ZHANGWentai ZHANGSun, 10 Jan 2010 08:38:00 GMThttp://www.cppblog.com/rchard/articles/105339.htmlhttp://www.cppblog.com/rchard/comments/105339.htmlhttp://www.cppblog.com/rchard/articles/105339.html#Feedback0http://www.cppblog.com/rchard/comments/commentRss/105339.htmlhttp://www.cppblog.com/rchard/services/trackbacks/105339.html令这个集合为S={x1,...,xn}，这里n>1，0<x1<...<xn。我们得到nx1<x1...xn<nxn，于是x1...xn<n，而x1...xn-1>=(n-1)!，所以n>(n-1)!>(n-1)(n-2)，解得2-√x<n<2+√2，于是n=2或3。又x1+...+xn=x1...xn，解得n=2时x1=x2=2，舍弃，所以n=3，易解得x1=1,x2=2,x3=3。问题得解。


Wentai ZHANG 2010-01-10 16:38 发表评论
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