Home Competitions AUSTRIAN-POLISH 1996 Problem 6
AUSTRIAN-POLISH 1996 Problem 6
Given natural numbers n > k > 1 n > k > 1 n > k > 1 x 1 , . . . , x n x_1,..., x_n x 1 , ... , x n x i 3 ( x i 2 + x i + 1 2 + . . . + x i + k − 1 2 ) = x i − 1 2 x_i^3(x_i^2 + x_{i+1}^2+... +x_{i+k-1}^2) = x_{i-1}^2 x i 3 ( x i 2 + x i + 1 2 + ... + x i + k − 1 2 ) = x i − 1 2 ≤ i ≤ n \le i \le n ≤ i ≤ n x n + i = x i x_{n+i} = x_i x n + i = x i i i i
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