Home Competitions RO-TST 1988 Problem 6
Find all vectors of n n n ( x 1 , x 2 , … , x n ) (x_1,x_2,\ldots,x_n) ( x 1 , x 2 , … , x n ) { x 1 = 1 x 2 + 1 x 3 + ⋯ + 1 x n x 2 = 1 x 1 + 1 x 3 + ⋯ + 1 x n ⋯ x n = 1 x 1 + 1 x 2 + ⋯ + 1 x n − 1 \left\{ \begin{array}{ccc} x_1 & = & \dfrac 1{x_2} + \dfrac 1{x_3} + \cdots + \dfrac 1{x_n } x_2 & = & \dfrac 1{x_1} + \dfrac 1{x_3} + \cdots + \dfrac 1{x_n} \ & \cdots & \ x_n & = & \dfrac 1{x_1} + \dfrac 1{x_2} + \cdots + \dfrac 1{x_{n-1}} \end{array} \right. { x 1 = x 2 1 + x 3 1 + ⋯ + x n 1 x 2 = x 1 1 + x 3 1 + ⋯ + x n 1 ⋯ x n = x 1 1 + x 2 1 + ⋯ + x n − 1 1 Mircea Becheanu
Dataset text AI-MO AoPS . Quoted with source.
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