Home Competitions ILL 1983 Problem 54
Find all solutions of the following system of n n n n n n x 1 ∣ x 1 ∣ − ( x 1 − a ) ∣ x 1 − a ∣ = x 2 ∣ x 2 ∣ , x 2 ∣ x 2 ∣ − ( x 2 − a ) ∣ x 2 − a ∣ = x 3 ∣ x 3 ∣ , ⋮ x n ∣ x n ∣ − ( x n − a ) ∣ x n − a ∣ = x 1 ∣ x 1 ∣ \begin{array}{c}\ x_1|x_1| - (x_1 - a)|x_1 - a| = x_2|x_2|,x_2|x_2| - (x_2 - a)|x_2 - a| = x_3|x_3|,\ \vdots \ x_n|x_n| - (x_n - a)|x_n - a| = x_1|x_1|\end{array} x 1 ∣ x 1 ∣ − ( x 1 − a ) ∣ x 1 − a ∣ = x 2 ∣ x 2 ∣ , x 2 ∣ x 2 ∣ − ( x 2 − a ) ∣ x 2 − a ∣ = x 3 ∣ x 3 ∣ , ⋮ x n ∣ x n ∣ − ( x n − a ) ∣ x n − a ∣ = x 1 ∣ x 1 ∣
where a a a
Dataset text AoPS wiki problems . Quoted with source.
Also ILL 1984 Problem 17 .
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