MathDB
GP free sets

Source: miklos schweitzer 2006 q6

September 3, 2021
geometric serieslimitreal analysis

Problem Statement

Let G (n) = max | A(n) |, where A(n) ranges over all subsets of {1,2,...,n} and contains no three-member geometric series, ie, there is no x,y,z∈Ax, y, z \in A such that x < y < z and xz = y^2. Prove that lim⁡n→∞G(n)n\lim_{n \to \infty} \frac{G (n)}{n} exists.
Back to ProblemsView on AoPS