Home Competitions BG-MO 1983 Problem 2
Let b 1 ≥ b 2 ≥ … ≥ b n b_1\ge b_2\ge\ldots\ge b_n b 1 ≥ b 2 ≥ … ≥ b n ( a 1 , a 2 , … , a n ) (a_1,a_2,\ldots,a_n) ( a 1 , a 2 , … , a n ) t ≥ 0 t\ge0 t ≥ 0 ( a 1 a 2 + t ) ( a 3 a 4 + t ) ⋯ ( a 2 n − 1 a 2 n + t ) ≤ ( b 1 b 2 + t ) ( b 3 b 4 + t ) ⋯ ( b 2 n − 1 b 2 n + t ) . (a_1a_2+t)(a_3a_4+t)\cdots(a_{2n-1}a_{2n}+t)\le(b_1b_2+t)(b_3b_4+t)\cdots(b_{2n-1}b_{2n}+t). ( a 1 a 2 + t ) ( a 3 a 4 + t ) ⋯ ( a 2 n − 1 a 2 n + t ) ≤ ( b 1 b 2 + t ) ( b 3 b 4 + t ) ⋯ ( b 2 n − 1 b 2 n + t ) .
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