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 28th British Mathematical Olympiad
1992年第28届英国奥林匹克数学竞赛
  1. p is an odd prime. Show that there are unique positive integers m, n such that m2 = n(n + p). Find m and n in terms of p .
  2. Show that 12/(w + x + y + z) ≤ 1/(w + x) + 1/(w + y) + 1/(w + z) + 1/(x + y) + 1/(x + z) + 1/(y + z) ≤ 3(1/w + 1/x + 1/y + 1/z)/4 for any positive reals w, x, y, z .
  3. The circumradius R of a triangle with sides a, b, c satisfies a2 + b2 = c2 - R2. Find the angles of the triangle .
  4. Each edge of a connected graph with n points is colored red, blue or green. Each point has exactly three edges, one red, one blue and one green. Show that n must be even and that such a colored graph is possible for any even n > 2. X is a subset of 1 < k < n points. In order to isolate X from the other points (so that there is no edge between a point in X and a point not in X) it is necessary and sufficient to delete R red edges, B blue edges and G green edges. Show that R, B, G are all even or all odd .
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