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第一天 (1993年1月7日8:00-12:30) 一、设n是奇数,试证存在2n个整数 a_1,a_2,…,a_n,b_1,b_2,…,b_n,使得对任意一个整数k,00,在下列条件下, k_1+k_2+…+k_r=k,k_i∈N,1≤r≤k.求a~k_1+a~k_2+…+a_r~k的最大值. 三、设圆k和k_1同心,它们的半径分别为R和R_1,R_1>R.四边形ABCD内接于圆k,四边形A_1B_1C_1D_1内接于圆k_1.点A_1,B_1,C_1,D_1分别在射线CD,DA,AB,BC上.求证
The first day (January 7, 1993, 8:00-12:30) First, let n be an odd number and testify that there are 2n integers a_1, a_2, ..., a_n, b_1, b_2, ..., b_n so that arbitrary An integer k, 00, under the following conditions, k_1 +k_2+...+k_r=k,k_i∈N,1≤r≤k. Find the maximum value of a~k_1+a~k_2+...+a_r~k. 3. Set the circle k and k_1 to be concentric. Their radii are R respectively. And R_1, R_1>R. The quadrangle ABCD is inscribed in the circle k, and the quadrilateral A_1B_1C_1D_1 is inscribed in the circle k_1. The points A_1, B_1, C_1, and D_1 are on the rays CD, DA, AB, and BC, respectively.