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 36th Canadian Mathematical Olympiads 2004年第36届加拿大数学奥林匹克 Find all ordered triples (x, y, z) of real numbers which satisfy the following system of equations: xy = z - x - y xz = y - x - z yz = x - y - z How many ways can 8 mutually non-attacking rooks be placed on a 9 × 9 chessboard so that all 8 rooks are on squares of the same colour ? [Two squares are said to be attacking each other if they are placed in the same row or column of the board.] Let A,B,C,D be four points on a circle (occurring in clockwise order), with AB < AD and BC > CD. Let the bisector of angle BAD meet the circle at X and the bisector of angle BCD meet the circle at Y . Consider the hexagon formed by these six points on the circle. If four of the six sides of the hexagon have equal length, prove that BD must be a diameter of the circle. Let p be an odd prime. Prove that ∑k from 1 to (p - 1) ( k^(2p+1)) ≡ p(p+1)/2 (mod p^2) [Note that a ≡ b (mod m) means that a - b is divisible by m.] (请原谅，我对有些公式使用了纯文本录入，但愿这没有影响您的阅读） Let T be the set of all positive integer divisors of 2004^100. What is the largest possible number of elements that a subset S of T can have if no element of S is an integer multiple of any other element of S ? 点此查看相关视频讲解 在方框内输入单词或词组