AMO-Bench 2025 Problem 18

Answer

Let complex numbers $z_1, z_2, \ldots, z_{2025}$ satisfy $\sum_{k=1}^{2025} z_k = 0, \sum_{k=1}^{2025} |z_k|^2 = 1.$ Find the minimum possible value of $\max_{1 \le i < j \le 2025} |z_i - z_j|.$

Dataset text AMO-Bench. Open licence.

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\frac{\sqrt{3}}{45}

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