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 The 28th British Mathematical Olympiad 1992年第28届英国奥林匹克数学竞赛 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 . 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 . The circumradius R of a triangle with sides a, b, c satisfies a2 + b2 = c2 - R2. Find the angles of the triangle . 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