MathDB
Inequality with lattice points

Source: Latvian TST for Baltic Way 2021 P4

September 25, 2021
inequalities

Problem Statement

Determine the smallest positive constant kk such that no matter what 33 lattice points we choose the following inequality holds: Lmax⁡−Lmin⁡≥1k⋅Lmax L_{\max} - L_{\min} \ge \frac{1}{\sqrt{k} \cdot L_{max}} where Lmax⁡L_{\max}, Lmin⁡L_{\min} is the maximal and minimal distance between chosen points.
Back to ProblemsView on AoPS