MathDB

P4

Part of 2021 Latvia Baltic Way TST

Problems(1)

Inequality with lattice points

Source: Latvian TST for Baltic Way 2021 P4

9/25/2021
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.
inequalities