Home Competitions CN-TST 2016 Problem 2
Find the smallest positive number λ \lambda λ z 1 , z 2 , z 3 ∈ { z ∈ C ∣ ∣ z ∣ < 1 } {z_1},{z_2},{z_3}\in\{z\in C\big| |z|<1\} z 1 , z 2 , z 3 ∈ { z ∈ C ∣ z ∣ < 1 } z 1 + z 2 + z 3 = 0 z_1+z_2+z_3=0 z 1 + z 2 + z 3 = 0 ∣ z 1 z 2 + z 2 z 3 + z 3 z 1 ∣ 2 + ∣ z 1 z 2 z 3 ∣ 2 < λ . \left|z_1z_2 +z_2z_3+z_3z_1\right|^2+\left|z_1z_2z_3\right|^2 <\lambda . ∣ z 1 z 2 + z 2 z 3 + z 3 z 1 ∣ 2 + ∣ z 1 z 2 z 3 ∣ 2 < λ .
Dataset text AI-MO AoPS . Quoted with source.
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