Let

As an application, we give a new proof of a result of Rédei-Megyesi about the number of directions determined by a set in a finite affine plane.

#### Keywords

- Uniform distribution
- affine plane

#### MSC 2010

- Primary: 05B25
- Secondary: 51E99

_{p} and a theorem of W. Burnside’s

Uniform Distribution of the Weighted Sum-of-Digits Functions Families of Well Approximable Measures The Inequality of Erdős-Turán-Koksma in the Terms of the Functions of the System Γ _{ℬs}On the Classification of Solutions of Quantum Functional Equations with Cyclic and Semi-Cyclic Supports Extreme Values of Euler-Kronecker Constants