奥数之家
奥数论坛
简短留言
| 首页 | 竞赛大纲 | 优秀前辈 | 视频提示 | 专题讲座 | 论文锦集 | 综合训练 | 修身养性 | 家教平台 | 奥数论坛 |
 
The 17th Balkan Mathematical Olympiad
2000年第17届巴尔干地区数学奥林匹克
  1. Find all real-valued functions on the reals which satisfy f( xf(x) + f(y) ) = f(x)2 + y for all x, y.
  2. ABC is an acute-angled triangle which is not isosceles. M is the midpoint of BC. X is any point on the segment AM. Y is the foot of the perpendicular from X to BC. Z is any point on the segment XY. U and V are the feet of the perpendiculars from Z to AB and AC. Show that the bisectors of angles UZV and UXV are parallel.
  3. How many 1 by 10√2 rectangles can be cut from a 50 x 90 rectangle using cuts parallel to its edges.
  4. Show that for any n we can find a set X of n distinct integers greater than 1, such that the average of the elements of any subset of X is a square, cube or higher power.
点击此处查看相关视频讲解
在方框内输入单词或词组
建议使用:IE 6.0及以上版本浏览器。不支持 Netscape浏览器。 本站空间由北京师范大学提供
Copyright © 2005-2007 aoshoo.com All Rights Reserved 滇ICP备05000048号
MSN:shuxvecheng@hotmail.com QQ:316180036 E-mail:aoshoo@sina.com 电话:15810289082