Home Competitions ILL 1977 Problem 38
Let m j > 0 m_j > 0 m j > 0 j = 1 , 2 , … , n j = 1, 2,\ldots, n j = 1 , 2 , … , n a 1 ≤ ⋯ ≤ a n < b 1 ≤ ⋯ ≤ b n < c 1 ≤ ⋯ ≤ c n a_1 \leq \cdots \leq a_n < b_1 \leq \cdots \leq b_n < c_1 \leq \cdots \leq c_n a 1 ≤ ⋯ ≤ a n < b 1 ≤ ⋯ ≤ b n < c 1 ≤ ⋯ ≤ c n ( ∑ j = 1 n m j ( a j + b j + c j ) ) 2 > 3 ( ∑ j = 1 n m j ) ( ∑ j = 1 n m j ( a j b j + b j c j + c j a j ) ) . \Biggl( \sum_{j=1}^{n} m_j(a_j+b_j+c_j) \Biggr)^2 > 3 \Biggl( \sum_{j=1}^{n} m_j \Biggr) \Biggl( \sum_{j=1}^{n} m_j(a_jb_j+b_jc_j+c_ja_j) \Biggr). ( j = 1 ∑ n m j ( a j + b j + c j ) ) 2 > 3 ( j = 1 ∑ n m j ) ( j = 1 ∑ n m j ( a j b j + b j c j + c j a j ) ) .
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