A cardinal number connected to the solvability of systems of difference equations in a given function class

Márton Elekes, Miklós Laczkovich

Let ${\mathbb{R}}^{\mathbb{R}}$ denote the set of real valued functions defined on the real line. A map $D:{\mathbb{R}}^{\mathbb{R}}\to {\mathbb{R}}^{\mathbb{R}}$ is a {\it difference operator}, if there are real numbers $a_i, b_i \ (i=1,…